Q&A Hero

Q: A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day: Successful Calls Probability 0 0.10 1 0.30 2 0.30 3 0.20 4 0.10 The expected number of successful sales calls per day is: A) 2.00 B) 1.15 C) 1.90 D) 2.50

Q: A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day: Successful Calls Probability 0 0.10 1 0.30 2 0.30 3 0.20 4 0.10 Based on this information, the probability that the sales rep will have a total of 2 successful calls in a two-day period is: A) 0.60 B) 0.09 C) 0.15 D) 0.06

Q: The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Accidents Probability 0 0.25 1 0.20 2 0.30 3 0.15 4 0.10 Based on this probability distribution, the standard deviation in the number of accidents per day is: A) 2.0 B) 1.63 C) 2.65 D) 1.28

Q: The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Accidents Probability 0 0.25 1 0.20 2 0.30 3 0.15 4 0.10 Based on this distribution, the expected number of accidents in a given day is: A) 0.30 B) 1.65 C) 2.00 D) 2.50

Q: The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Accidents Probability 0 0.25 1 0.20 2 0.30 3 0.15 4 0.10 This distribution is an example of: A) a uniform distribution. B) a continuous probability distribution. C) a discrete probability distribution. D) an expected value distribution.

Q: The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Accidents Probability 0 0.25 1 0.20 2 0.30 3 0.15 4 0.10 The probability of having less than 2 accidents on a given day is: A) 0.30 B) 0.75 C) 0.45 D) 0.25

Q: When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is hypergeometric.

Q: A company has 20 cars that are available for use by company executives for official business purposes. Six of these cars are SUVs, 8 are luxury type cars, and the rest are basic sedans. Suppose the cars are randomly assigned each week. If 5 cars are put into use, the chance that none of the SUVs or luxury cars will be in the group is approximately .0004.

Q: The city council consists of 3 Democrats, 5 Republicans and 3 independents. Subcommittees are supposed to be randomly assigned from the council. Suppose the 5-member planning and zoning subcommittee is composed of 3 Democrats and 2 Republicans. The probability of this happening by chance alone is approximately .4545.

Q: A warehouse contains 5 parts made by the Stafford Company and 8 parts made by the Wilson Company. If an employee selects 3 of the parts from the warehouse at random, the probability that all 3 parts are from the Wilson Company is approximately .1958.

Q: A warehouse contains 5 parts made by the Stafford Company and 8 parts made by the Wilson Company. If an employee selects 3 of the parts from the warehouse at random, the probability that none of the 3 parts is from the Wilson Company is approximately .03496.

Q: The primary application for the hypergeometric probability distribution is in situations where the sampling is done without replacement from a finite population.

Q: The makers of Crustfree Bread in Boston have a quality standard that allows for no more than 3 burned loaves per batch on average. Assuming that the average of 3 per batch is being met, the standard deviation for the number of burned loaves in 4 batches is approximately 1.73 loaves.

Q: The makers of Crustfree Bread in Boston have a quality standard that allows no more than 3 burned loaves per batch on average. Recently, the manager inspected a batch and found 5 burned loaves. She did not appear to be upset at the production meeting. This is because the chance of exactly 5 burned loaves occurring is 0.1008.

Q: The Brockingham Carpet Company prides itself on high quality carpets. At the end of each day, the company quality managers select 3 square yards for inspection. The quality standard requires an average of no more than 2.3 defects per square yard. Last night, the inspector found 8 defects in the sample of 3 square yards. The chance of finding 8 or more defects in the sample is 0.9975.

Q: The Brockingham Carpet Company prides itself on high quality carpets. At the end of each day, the company quality managers select 3 square yards for inspection. The quality standard requires an average of no more than 2.3 defects per square yard. The expected number of defects that the inspector will find during the inspection is 6.9.

Q: The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that between 2 and 3 customers inclusively will arrive in one hour is 0.0263.

Q: The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that more than 4 customers will arrive in a 30-minute period is 0.1933.

Q: The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that exactly 8 customers will arrive in a one-hour period is 0.1366.

Q: The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, the standard deviation for the call distribution is about 3.87 calls.

Q: The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, the expected number of calls in the first 30 minutes is 7.5 calls.

Q: The primary difference between the binomial distribution and the Poisson distribution is that the Poisson is used to describe a continuous random variable and the binomial is used for discrete random variables.

Q: The probability of the outcome changes from trial to trial in a binomial experiment.

Q: The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will end up being 100 percent inspected is approximately .0746.

Q: The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that contains twice the amount of defects allowed by the contract requirements will be shipped without further inspection is approximately .3874.

Q: The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will be shipped without further inspection is approximately .9139.

Q: A company has 20 copy machines and every day there is a 5 percent chance for each machine that it will not be working that day. If the company wants to calculate the probability of, say, 2 machines not working, it should use the Poisson distribution.

Q: A direct marketing company believes that the probability of making a sale when a call is made to an individual's home is .02. The probability of making 2 or 3 sales in a sample of 20 calls is .0593.

Q: The number of defects discovered in a random sample of 100 products produced at the Berdan Manufacturing Company is binomially distributed with p = .03. Based on this, the standard deviation of the number of defects per sample of size 100 is 2.91.

Q: One difference between the binomial distribution and Poisson distribution is that the binomial's upper bound is the number of trials while the Poisson has no particular upper bound.

Q: The distribution for the number of emergency calls to a city's 911 emergency number in a one-hour time period is likely to be described by a binomial distribution.

Q: The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the probability that fewer than 5 customers will request smoking rooms is approximately 0.09.

Q: The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the probability that more than 20 customers in the sample will request nonsmoking rooms is approximately 0.09.

Q: The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the standard deviation of requests for nonsmoking rooms is 5.25 customers.

Q: The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the expected number of requests for nonsmoking rooms is 14.

Q: When using the binomial distribution, the maximum possible number of success is the number of trials.

Q: Ace Computer Manufacturer buys disk drives in lots of 5,000 units from a supplier in California. The contract calls for, at most, 3 percent of the disk drives to be defective. When a shipment arrives, a sample of n = 15 parts is selected. If zero defects are found in this sample, the shipment is accepted. If 3 or more defects are found, the shipment is rejected and sent back to the supplier. If the number of defects found is 1 or 2, a second sample of 15 parts is selected. If this sample yields 1 or fewer defects, the shipment is accepted; otherwise the shipment is rejected. Based on a binomial distribution, the probability that Ace will reject a shipment of parts that meets the contract requirements is approximately 0.0355.

Q: A pizza restaurant uses 7 different toppings on its pizzas. At lunch time it has a pizza buffet and makes pizzas with 2 toppings. If it wants to serve every possible combination of 2 toppings, it would need to make 14 different pizzas.

Q: Each week American Stores receives a shipment from a supplier. The contract specifies that the maximum allowable percent defective is 5 percent. When the shipment arrives, a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution. The probability that the shipment is accepted is approximately 0.81

Q: Each week American Stores receives a shipment from a supplier. The contract specifies that the maximum allowable percent defective is 5 percent. When the shipment arrives, a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution. The probability that the shipment is rejected is approximately 0.19.

Q: One of the characteristics of the binomial distribution is that the probability of success for each trial depends on whether the previous trial was a success or not.

Q: Bill Price is a sales rep in northern California representing a line of athletic socks. Each day, he makes 10 sales calls. The chance of making a sale on each call is thought to be 0.30. The probability that he will make exactly two sales is approximately 0.2335.

Q: Six managers at a company all enjoy golf. Each Saturday, four of the six get together for 18 holes of golf. They have decided to set up a schedule so that the same foursome does not play twice before all possible foursomes have played. The number of weekends that will pass before the same group would play twice is 15.

Q: A construction company has found it has a probability of 0.10 of winning each time it bids on a project. The probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution.

Q: The Ace Construction Company has entered into a contract to widen a street in Boston. The possible payoffs for this project have been determined by management. The probabilities for these payoffs could be determined using a binomial distribution.

Q: In a Florida town, the probability distribution for the number of legitimate emergency calls per day for the Fire Department is given as follows. Also shown is the probability distribution for the number of false alarms: Given this information, the expected number of total calls to the fire department is 1.60 calls.

Q: Holmstead Company owns two small engine repair stores. The expected value of the number of complaints received per month at store 1 is 4.5 complaints. Further, the expected number of complaints per month for store 1 and store 2 combined is 13.6. This means the expected number of complaints per month at store 2 must be 9.1 complaints.

Q: The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Injured Skiers Probability 0 0.05 1 0.15 2 0.40 3 0.30 4 0.10 Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

Q: The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Injured Skiers Probability 0 0.05 1 0.15 2 0.40 3 0.30 4 0.10 Based on this information, the expected number of injuries per weekend is 2.25.

Q: The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: No-shows Probability 0 0.30 1 0.20 2 0.20 3 0.15 4 0.15 Based on this information, the standard deviation for the number of no-shows is about 0.36 customers.

Q: The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: No-shows Probability 0 0.30 1 0.20 2 0.20 3 0.15 4 0.15 Based on this information, the most likely number of no-shows on any given day is 0 customers.

Q: The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: No-shows Probability 0 0.30 1 0.20 2 0.20 3 0.15 4 0.15 Based on this information, the expected number of no-shows is 1.65 customers.

Q: The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road. The following table shows the probability distribution for the profit that could occur if it takes the contract: Profit Probability $30,000 0.15 $50,000 0.20 $70,000 0.30 $100,000 0.35 Based on this information, the profit standard deviation for the company if it takes the contract is $11,235.

Q: The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road. The following table shows the probability distribution for the profit that could occur if it takes the contract: Profit Probability $30,000 0.15 $50,000 0.20 $70,000 0.30 $100,000 0.35 Based on this information, the probability of profit being at least $50,000 is 0.50.

Q: A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher standard deviation.

Q: The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road. The following table shows the probability distribution for the profit that could occur if it takes the contract: Profit Probability $30,000 0.15 $50,000 0.20 $70,000 0.30 $100,000 0.35 Based on this information, the expected profit for the company if it takes the contract is $60,000.

Q: The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road. The following table shows the probability distribution for the profit that could occur if it takes the contract: Profit Probability $30,000 0.15 $50,000 0.20 $70,000 0.30 $100,000 0.35 Based on this information, the expected profit for the company if it takes the contract is $70,500.

Q: The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road. The following table shows the probability distribution for the profit that could occur if it takes the contract: Profit Probability $30,000 0.15 $50,000 0.20 $70,000 0.30 $100,000 0.35 Based on this information, the probability of profit being at least $70,000 is 0.65.

Q: The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week. Then the variable, number of showings, is a continuous distribution.

Q: The time required to assemble two components into a finished part is recorded for each employee at the plant. The resulting random variable is an example of a continuous random variable.

Q: When a market research manager records the number of potential customers who were surveyed indicating that they like the product design, the random variable, number who like the design, is a discrete random variable.

Q: The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

Q: When a single value is randomly chosen from a discrete distribution, the different possible values are mutually exclusive.

Q: The random variable, number of customers entering a store between 9 AM and noon, is an example of a discrete random variable.

Q: If a random variable is discrete, it means that the outcome for the random variable can take on only one of two possible values.

Q: The only two types of random variables are discrete and continuous random variables.

Q: A random variable is generated when a variable's value is determined by using classical probability.

Q: The Anderson Lumber Company has three sawmills that produce boards of different lengths. The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Based on these data, the probability of selecting a board from inventory that is 10 feet long is: A) 0.196 B) 0.450 C) 0.084 D) 0.170

Q: The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data, if a player has a handicap that is 10 or more, the probability that he or she will use a Nike golf ball is: A) 0.21 B) 0.10 C) 0.45 D) 0.48

Q: The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data, the probability of someone using a Strata ball and having a handicap under 2 is: A) 0.05 B) 0.38 C) 0.25 D) None of the above

Q: The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: If a player comes to the course using a Nike golf ball, the probability that he or she has a handicap of at least 10 is: A) 0.22 B) 0.48 C) slightly greater than 0.45 D) 0.10

Q: The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data, the probability that a player will use a Strata golf ball is: A) 0.15 B) 0.20 C) 0.18 D) None of the above

Q: The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data, the probability of a golfer having a handicap less than 10 is: A) 0.52 B) 0.10 C) 0.34 D) None of the above

Q: If two events are independent, then A) they must be mutually exclusive. B) the sum of their probabilities must be equal to one. C) their intersection must be zero. D) None of the above

Q: When a pair of dice are rolled, the outcome for each die can be said to be: A) mutually exclusive. B) mutually inclusive. C) dependent. D) independent.

Q: When a customer enters a store there are three outcomes that can occur: buy nothing, buy a small amount, or buy a large amount. In this situation, if a customer buys a large amount, he or she cannot also buy a small amount or buy nothing. Thus the events are: A) independent. B) mutually exclusive. C) all inclusive. D) dependent events.

Q: A study was recently done in which 500 people were asked to indicate their preferences for one of three products. The following table shows the breakdown of the responses by gender of the respondents. Suppose one person is randomly chosen. Based on this data, what is the probability that the person chosen is a female who prefers product C? A) 0.24 B) 0.86 C) 0.92 D) 0.31

Q: A study was recently done in which 500 people were asked to indicate their preferences for one of three products. The following table shows the breakdown of the responses by gender of the respondents. Based on these data, the probability that a person in the population will prefer product A can be assessed as: A) 0.18 B) 0.56 C) 0.286 D) 0.16

Q: A study was recently done in which 500 people were asked to indicate their preferences for one of three products. The following table shows the breakdown of the responses by gender of the respondents. If the people conducting the study wish to assess the probability that product A will be preferred by members of the target population, the method of assessment to be used would most likely be: A) classical probability assessment. B) subjective assessment. C) relative frequency of occurrence. D) independent events.

Q: A consumer products company is planning to introduce a new product. The method that is least likely to be used to assess the probability of the product being successful is: A) classical probability assessment. B) subjective assessment. C) relative frequency of occurrence. D) elementary events.