Computer Science

Q: NARRBEGIN: SA_92_96The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars. AudienceFormat A1A2A3Rock$ 110$ 80$ 70Country$ 90$ 120$ 50Rap$ 70$ 60$ 140Probability0.30.50.2NARRENDWhat format is optimal? What is the expected profit in that case?

Q: NARRBEGIN: SA_92_96The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars. AudienceFormat A1A2A3Rock$ 110$ 80$ 70Country$ 90$ 120$ 50Rap$ 70$ 60$ 140Probability0.30.50.2NARRENDConstruct a decision tree to help the station identify its optimal format. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

Q: NARRBEGIN: SA_90_91The following is a payoff table giving profits for various situations: States of NatureABCAlternative 1160120140Alternative 215014090Alternative 312016080Do Nothing000The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively.NARRENDWhat else might one consider in choosing from among these alternatives?

Q: NARRBEGIN: SA_90_91The following is a payoff table giving profits for various situations: States of Nature ABCAlternative 1160120140Alternative 215014090Alternative 312016080Do Nothing000The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively.NARRENDWhat are the expected payoffs for the three alternatives?

Q: NARRBEGIN: SA_86_89A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.Demand (in hundreds)Probability40.3050.5060.20NARRENDGenerate a risk profile for each possible decision in this problem. Would this have any impact on your decision?

Q: NARRBEGIN: SA_86_89A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.Demand (in hundreds)Probability40.3050.5060.20NARRENDWhat is the optimal strategy for order quantity, and what is the expected profit in that case?

Q: NARRBEGIN: SA_86_89A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.Demand (in hundreds)Probability40.3050.5060.20NARRENDConstruct a decision tree to identify the buyer's course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year.

Q: NARRBEGIN: SA_86_89A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.Demand (in hundreds)Probability40.3050.5060.20NARRENDFormulate a payoff table that specifies the contribution to profit (in dollars) from the sales of footballs by this chain for each possible purchase decision (in hundreds of pairs) and each outcome with respect to consumer demand.

Q: NARRBEGIN: SA_83_85 A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year. NARREND If a randomly selected individual is observed to earn less than $50,000 per year, what is the probability that this person is a woman?

Q: NARRBEGIN: SA_83_85 A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year. NARREND If a randomly selected individual is observed to earn at least $50,000 per year, what is the probability that this person is a man?

Q: NARRBEGIN: SA_83_85 A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year. NARREND What is the probability that a randomly selected individual from this population earns less than $50,000 per year?

Q: NARRBEGIN: SA_79_82The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC's alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC's marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below.MKT expandsMKT stableMKT contractsBuild new plant$1,650,000$1,000,000$450,000Expand plant$1,000,000$850,000$450,000Do nothing$0$0$0NARRENDGenerate a risk profile for each of WTC's possible decisions in this problem. Characterize the differences in risk for the different options.

Q: NARRBEGIN: SA_79_82The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC's alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC's marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below. MKT expandsMKT stableMKT contractsBuild new plant$1,650,000$1,000,000$450,000Expand plant$1,000,000$850,000$450,000Do nothing$0$0$0NARRENDWhat course of action is optimal for WTC? What is the expected profit in that case?

Q: Construct a decision tree to identify the course of action that maximizes WTC's expected profit. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

Q: NARRBEGIN: SA_79_82The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC's alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC's marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below. MKT expandsMKT stableMKT contractsBuild new plant$1,650,000$1,000,000$450,000Expand plant$1,000,000$850,000$450,000Do nothing$0$0$0NARRENDFormulate a payoff table that specifies WTC's payoff (in dollars) associated with each possible decision and each market condition in the future.

Q: NARRBEGIN: SA_74_78 A nuclear power company is deciding whether to build a nuclear plant at Chico Canyon or at Pleasantville. The cost of building the power plant is $14 million at Chico and $20 million at Pleasantville. If the company builds at Chico, however, and an earthquake occurs at Chico during the next 5 years, construction will be terminated and the company will lose $14 million (and will still have to build a power plant at Pleasantville). Without further information, the company believes there is a 20% chance that an earthquake will occur at Chico during the next 5 years. NARREND (A) Construct a decision tree to help the power company decide what to do. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (B) Where should the power company build the plant? What is the expected cost? (C) Suppose that a geologist (and his team) can be hired to analyze the fault structure at Chico Canyon. He will either predict whether an earthquake will occur or not. If the geologist is perfectly reliable, what is the most the company should be willing to pay for his services? (D) Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist's past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions? (E) Should the company hire the geologist if his fee is $1.5M?

Q: Tyson Manufacturing (a maker of industrial products) is interested in marketing a new product. The company must decide whether to manufacture this product essentially on its own or employ a subcontractor to manufacture it. Below are two tables that represent the information related to the estimated probability distribution of the cost of one unit of this product under each alternative. Cost under "Make" alternative. Cost under "Buy" alternative. Cost per unit Probability Cost per unit Probability $40 0.20 $40 0.15 $45 0.25 $45 0.30 $50 0.35 $50 0.40 $55 0.20 $55 0.15 Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of buying the new product, should the company make the new product or buy it from a subcontractor? Show your work.

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND What is the probability that X is at most 2?

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND What is the probability that X is between 1 and 3?

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND Find the mean and standard deviation of X.

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND What is the distribution of X and what are the parameters?

Q: NARRBEGIN: SA_117_120 The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes. NARREND What is the probability that it will take a technician between 10 to 15 minutes to fix a computer problem?

Q: NARRBEGIN: SA_117_120 The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes. NARREND What is the variance of the time it takes a technician to fix a computer problem?

Q: NARRBEGIN: SA_117_120 The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes. NARREND What is the probability density function for the time it takes a technician to fix a computer problem?

Q: NARRBEGIN: SA_115_116 A used car salesman in a small town states that, on the average, it takes him 5 days to sell a car. Assume that the probability distribution of the length of time between sales is exponentially distributed. NARREND What is the probability that he will have to wait between 6 and 10 days before making another sale?

Q: NARRBEGIN: SA_112_114 The number of arrivals at a local gas station between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12. NARREND Find the probability that the number of arrivals between 4:00 and 5:00 P.M. is exactly two.

Q: NARRBEGIN: SA_107_111 Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour. Let X represent the number of customers arriving per hour. The probabilities associated with X are shown below. P(X < 5) = 0.0000, P(X < 10) = 0.0000, P(X < 15) = 0.0009, P(X < 20) = 0.0219, P(X < 25) = 0.1572, P(X < 30) = 0.4757 P(X = 30) = 0.0726, P(X = 31) = 0.0703, P(X = 32) = 0.0659, P(X = 33) = 0.0599, P(X = 34) = 0.0529, P(X = 35) = 0.0453 NARREND What is the probability that the number of customers who arrive at this checkout counter in a given hour will be greater than 35?

Q: NARRBEGIN: SA_107_111 Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour. Let X represent the number of customers arriving per hour. The probabilities associated with X are shown below. P(X < 5) = 0.0000, P(X < 10) = 0.0000, P(X < 15) = 0.0009, P(X < 20) = 0.0219, P(X < 25) = 0.1572, P(X < 30) = 0.4757 P(X = 30) = 0.0726, P(X = 31) = 0.0703, P(X = 32) = 0.0659, P(X = 33) = 0.0599, P(X = 34) = 0.0529, P(X = 35) = 0.0453 NARREND What is the probability that fewer than 33 customers arrive at this checkout counter in a given hour?

Q: NARRBEGIN: SA_107_111 Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour. Let X represent the number of customers arriving per hour. The probabilities associated with X are shown below. P(X < 5) = 0.0000, P(X < 10) = 0.0000, P(X < 15) = 0.0009, P(X < 20) = 0.0219, P(X < 25) = 0.1572, P(X < 30) = 0.4757 P(X = 30) = 0.0726, P(X = 31) = 0.0703, P(X = 32) = 0.0659, P(X = 33) = 0.0599, P(X = 34) = 0.0529, P(X = 35) = 0.0453 NARREND What is the probability that at least 20 customers, but fewer than 30 customers arrive at this checkout counter in a given hour?

Q: NARRBEGIN: SA_107_111 Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour. Let X represent the number of customers arriving per hour. The probabilities associated with X are shown below. P(X < 5) = 0.0000, P(X < 10) = 0.0000, P(X < 15) = 0.0009, P(X < 20) = 0.0219, P(X < 25) = 0.1572, P(X < 30) = 0.4757 P(X = 30) = 0.0726, P(X = 31) = 0.0703, P(X = 32) = 0.0659, P(X = 33) = 0.0599, P(X = 34) = 0.0529, P(X = 35) = 0.0453 NARREND What is the probability that at least 25 customers arrive at this checkout counter in a given hour?

Q: NARRBEGIN: SA_104_106 A large retailer has purchased 10,000 DVDs. The retailer is assured by the supplier that the shipment contains no more than 1% defective DVDs (according to agreed specifications). To check the supplier's claim, the retailer randomly selects 100 DVDs and finds six of the 100 to be defective. NARREND (A) Assuming the supplier's claim is true, compute the mean and the standard deviation of the number of defective DVDs in the sample. (B) Based on your answer to (A), is it likely that as many as six DVDs would be found to be defective, if the claim is correct? (C) Suppose that six DVDs are indeed found to be defective. Based on your answer to (A), what might be a reasonable inference about the manufacturer's claim for this shipment of 10,000 DVDs?

Q: NARRBEGIN: SA_101_103 Past experience indicates that 20% of all freshman college students taking an intermediate algebra course withdraw from the class. NARREND (A) Using the binomial distribution, find the probability that 6 or more of the 30 students taking this course in a given semester will withdraw from the class. (B) Using the normal approximation to the binomial, find the probability that 6 or more of the 30 students taking this course in a given semester will withdraw from the class. (C) Compare the results obtained in (A) and (B). Under what conditions will the normal approximation to this binomial probability become even more accurate?

Q: NARRBEGIN: SA_95_100 A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. NARREND Suppose that an highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. How many traffic violations would be found in a shift?

Q: NARRBEGIN: SA_91_94Consider a binomial random variable X withn = 5 and p = 0.40.NARRENDFind the mean and the variance of X.

Q: NARRBEGIN: SA_91_94Consider a binomial random variable X withn = 5 and p = 0.40.NARRENDFind P(2X4).

Q: NARRBEGIN: SA_91_94Consider a binomial random variable X withn = 5 and p = 0.40.NARRENDFind P(X < 3).

Q: NARRBEGIN: SA_91_94Consider a binomial random variable X withn = 5andp = 0.40.NARRENDFind the probability distribution of X.

Q: NARRBEGIN: SA_79_90The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.NARRENDWhat is the standard deviation of the number of the new microwaves sold that will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the expected number of the new microwaves sold that will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that between three and six (exclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that between two and four (inclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that at least one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that more than one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?

Q: NARRBEGIN: SA_76_78 A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. NARREND Only 5% of the students taking the test scored higher than what value?

Q: NARRBEGIN: SA_76_78 A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. NARREND What is the probability of getting a score higher than 85 on this exam?

Q: NARRBEGIN: SA_76_78 A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. NARREND What percentage of students scored between 81 and 89 on this exam?

Q: Why is the independence assumption in Question 74 probably not realistic? Using a more realistic assumption, do you think the probability in Question 74 would increase or decrease?

Q: NARRBEGIN: SA_71_75 Wendy's fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. Use this information to answer the following questions. NARREND If the restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day, what is the probability that it will run out of hamburgers or chicken sandwiches (or both) that day? Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent.

Q: NARRBEGIN: SA_71_75 Wendy's fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. Use this information to answer the following questions. NARREND How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?

Q: NARRBEGIN: SA_71_75 Wendy's fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. Use this information to answer the following questions. NARREND How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day?

Q: NARRBEGIN: SA_66_71 The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions. Probability Calculations P(Sales < 2,000,000) = 0.134, P(Sales < 2,050,000) = 0.339 P(Sales < 2,100,000) = 0.609, P(Sales < 2,150,000) = 0.834 Percentiles Calculations 1st percentile = 1,912,245, 5th percentile = 1,961,388 95th percentile = 2,198,612, 99th percentile = 2,247,755 NARREND What number of cars, equidistant from the mean, such that 98% of car sales are between these values?

Q: NARRBEGIN: SA_66_71 The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions. Probability Calculations P(Sales < 2,000,000) = 0.134, P(Sales < 2,050,000) = 0.339 P(Sales < 2,100,000) = 0.609, P(Sales < 2,150,000) = 0.834 Percentiles Calculations 1st percentile = 1,912,245, 5th percentile = 1,961,388 95th percentile = 2,198,612, 99th percentile = 2,247,755 NARREND What is the probability that this company will sell between 2.0 and 2.15 million cars next year?

Q: NARRBEGIN: SA_66_71 The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions. Probability Calculations P(Sales < 2,000,000) = 0.134, P(Sales < 2,050,000) = 0.339 P(Sales < 2,100,000) = 0.609, P(Sales < 2,150,000) = 0.834 Percentiles Calculations 1st percentile = 1,912,245, 5th percentile = 1,961,388 95th percentile = 2,198,612, 99th percentile = 2,247,755 NARREND What is the probability that this company will sell more than 2 million cars next year?

Q: NARRBEGIN: SA_66_71 The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions. Probability Calculations P(Sales < 2,000,000) = 0.134, P(Sales < 2,050,000) = 0.339 P(Sales < 2,100,000) = 0.609, P(Sales < 2,150,000) = 0.834 Percentiles Calculations 1st percentile = 1,912,245, 5th percentile = 1,961,388 95th percentile = 2,198,612, 99th percentile = 2,247,755 NARREND There is a 1% chance that this company will sell more than what number of cars during the next year?

Q: NARRBEGIN: SA_66_71 The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions. Probability Calculations P(Sales < 2,000,000) = 0.134, P(Sales < 2,050,000) = 0.339 P(Sales < 2,100,000) = 0.609, P(Sales < 2,150,000) = 0.834 Percentiles Calculations 1st percentile = 1,912,245, 5th percentile = 1,961,388 95th percentile = 2,198,612, 99th percentile = 2,247,755 NARREND Calculate the mean, variance, and standard deviation for the entire year (assume 52 weeks in the year).

Q: NARRBEGIN: SA_64_65 The height of a typical American male adult is normally distributed with a mean of 68 inches and a standard deviation of 5 inches. We observe the heights of 12 American male adults. NARREND Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean and standard deviation of Y.

Q: NARRBEGIN: SA_64_65 The height of a typical American male adult is normally distributed with a mean of 68 inches and a standard deviation of 5 inches. We observe the heights of 12 American male adults. NARREND What is the probability that exactly half the male adults will be less than 62 inches tall?

Q: NARRBEGIN: SA_62_63The weekly demand for General Motors (GM) car sales follows a normal distribution with a mean of 40,000 cars and a standard deviation of 12,000 cars.NARRENDWhat is the probability that GM will sell between 2.0 and 2.3 million cars during the next year?

Q: NARRBEGIN: SA_62_63The weekly demand for General Motors (GM) car sales follows a normal distribution with a mean of 40,000 cars and a standard deviation of 12,000 cars.NARRENDThere is a 5% chance that GM will sell more than what number of cars during the next year?

Q: NARRBEGIN: SA_56_61A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts.Probability CalculationsP(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133,P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711Percentiles Calculations1st Percentile = $9.06, 5th Percentile = $15.20,95th Percentile = $44.80, 99th Percentile = $50.94NARRENDWhat two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?

Q: NARRBEGIN: SA_56_61 A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts. Probability Calculations P(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133, P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711 Percentiles Calculations 1st Percentile = $9.06, 5th Percentile = $15.20, 95th Percentile = $44.80, 99th Percentile = $50.94 NARREND What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?

Q: NARRBEGIN: SA_56_61 A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts. Probability Calculations P(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133, P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711 Percentiles Calculations 1st Percentile = $9.06, 5th Percentile = $15.20, 95th Percentile = $44.80, 99th Percentile = $50.94 NARREND What is the probability that a randomly selected customer will spend between $20 and $35?

Q: NARRBEGIN: SA_56_61 A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts. Probability Calculations P(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133, P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711 Percentiles Calculations 1st Percentile = $9.06, 5th Percentile = $15.20, 95th Percentile = $44.80, 99th Percentile = $50.94 NARREND What is the probability that a randomly selected customer will spend $30 or more?

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