Q&A Hero

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 $20 or more?

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 is the probability that a randomly selected customer will spend less than $15?

Q: Using the standard normal curve, the Z- score representing the 10th percentile is 1.28.

Q: The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Q: The Poisson random variable is a discrete random variable with infinitely many possible values.

Q: The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Q: The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

Q: A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z- score is "0.50.

Q: Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.

Q: The mean and standard deviation of a normally distributed random variable which has been "standardized" are zero and one, respectively.

Q: Using the standard normal distribution, the Z- score representing the 99th percentile is 2.326.

Q: A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

Q: The binomial random variable represents the number of successes that occur in a specific period of time.

Q: An exponential distribution with parameter = 0.2 has mean and standard deviation both equal to 5.

Q: The Poisson distribution is characterized by a single parameter, which must be positive.

Q: For a given probability of success p that is not too close to 0 or 1, the binomial distribution tends to take on more of a symmetric bell shape as the number of trials n increases.

Q: A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance if np > 5 and n(1-p) > 5.

Q: The binomial distribution is a discrete distribution that deals with a sequence of identical trials, each of which has only two possible outcomes.

Q: The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.

Q: Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

Q: The Poisson probability distribution is one of the most commonly used continuous probability distributions.

Q: Using the standard normal distribution, the Z-score representing the 5th percentile is 1.645.

Q: Much of the study of probabilistic inventory models, queuing models, and reliability models relies heavily on the Poisson and Exponential distributions.

Q: If the random variable X is normally distributed with mean and standard deviation , then the random variable Z defined by is also normally distributed with mean 0 and standard deviation 1.

Q: The variance of a binomial distribution is given by the formula, where n is the number of trials, and p is the probability of success in any trial.

Q: The number of loan defaults per month at a bank is Poisson distributed.

Q: The total area under the normal distribution curve is equal to one.

Q: If the mean of an exponential distribution is 2, then the value of the parameter is a. 4 b. 2 c. 1 d. 0.5

Q: Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter? a. Uniform b. Normal c. Exponential d. Poisson

Q: The Poisson and Exponential distributions are commonly used in which of the following applications a. Inventory models b. Financial models c. Failure analysis models d. All of these options

Q: Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85X 90) is a. 0.5328 b. 0.3413 c. 0.1915 d. 0.1498

Q: If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to a. 10 b. 13 c. 30 d. 90

Q: If the random variable X is exponentially distributed with parameter = 1.5, then P(2X 4), up to 4 decimal places, is a. 0.6667 b. 0.0473 c. 0.5000 d. 0.2500

Q: If the random variable X is exponentially distributed with parameter = 3, then P(X 2) , up to 4 decimal places , is a. 0.3333 b. 0.5000 c. 0.6667 d. 0.0025

Q: Given that Z is a standard normal variable, the value z for which P(Z z) = 0.2580 is a. 0.70 b. 0.758 c. -0.65 d. 0.242

Q: Given that Z is a standard normal random variable, P(-1.0Z1.5) is a. 0.7745 b. 0.8413 c. 0.0919 d. 0.9332

Q: The binomial probability distribution is used with a. a discrete random variable b. a continuous random variable c. either a discrete or a continuous random variable, depending on the variance d. either a discrete or a continuous random variable, depending on the sample size

Q: The variance of a binomial distribution for which n = 100 and p = 0.20 is: a. 100 b. 80 c. 20 d. 16

Q: Which of the following might not be appropriately modeled with a normal distribution? a. The daily low temperature in Anchorage, Alaska b. The returns on a stock c. The daily change in inventory at a computer manufacturer d. The salaries of employees at a large company

Q: Which probability distribution applies to the number of events occurring within a specified period of time or space a. Binomial distribution b. Poisson distribution c. Any discrete probability distribution d. Any continuous probability distribution

Q: The Poisson random variable is a: a. discrete random variable with infinitely many possible values b. discrete random variable with finite number of possible values c. continuous random variable with infinitely many possible values d. continuous random variable with finite number of possible values

Q: Sampling done withoutreplacement means that a. only certain members of the population can be sampled b. each member of the population can be sampled repeatedly c. each member of the population can be sampled only once d. each member of the population can be sampled twice

Q: The standard normal distribution has a mean and a standard deviation respectively equal to a. 0 and 0 b. 1 and 1 c. 1 and 0 d. 0 and 1

Q: A Poisson distribution is: a. relevant when we sample from a population with only two types of members. b. relevant when we perform a series of independent, identical experiments with only two possible outcomes. c. usually relevant when we are interested in the number of events that occur over a given interval of time d. the cornerstone of statistical theory e. All of the above

Q: Which of the following equations shows the process of standardizing? a. b. c. d.

Q: A continuous probability distribution is characterized by: a. a list of possible values b. counts c. an array of individual values d. a continuum of possible values

Q: If we plot a continuous probability distribution f(x), the total probability under the curve is a. -1 b. 0 c. 1 d. 100

Q: The mean of a probability distribution is a: a. measure of variability of the distribution b. measure of central location c. measure of relative likelihood d. measure of skewness of the distribution

Q: The standard deviation of a probability distribution is a: a. measure of variability of the distribution b. measure of central location c. measure of relative likelihood d. measure of skewness of the distribution

Q: The normal distribution is: a. a discrete distribution with two parameters b. a binomial distribution with only one parameter c. a density function of a discrete random variable d. a continuous distribution with two parameters

Q: If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean? a. equal to the mean b. to the left of the mean c. to the right of the mean d. None of the above

Q: One reason for standardizing random variables is to measure variables with: a. different means and standard deviations on a non-standard scale b. different means and standard deviations on a single scale c. dissimilar means and standard deviations in like terms d. similar means and standard deviations on two scales

Q: We assume that the outcomes of successive trials in a binomial experiment are: a. probabilistically independent b. probabilistically dependent c. identical from trial to trial d. random number between 0 and 1

Q: Tossing a coin is an example of a (n) a. binomial distribution b. normal distribution c. exponential distribution d. Poisson distribution

Q: The higher the value of the density function f(x), a. the less likely the value x b. the more likely the value x c. the less likely the distribution is normal d. None of the above

Q: The law of large numbers states that subjective probabilities can be estimated based on the long run relative frequencies of events

Q: When we wish to determine the probability that at least one of several events will occur, we would use the addition rule.

Q: Conditional probability is the probability that an event will occur, with no other events taken into consideration.

Q: If P(A and B) = 1, then A and B must be collectively exhaustive.

Q: The probability that event A will not occur is denoted as .

Q: If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

Q: Probability is a number between 0 and 1, inclusive, which measures the likelihood that some event will occur.

Q: Two events A and B are said to be independent if P(A andB)=P(A) +P(B)

Q: The number of cars produced by GM during a given quarter is a continuous random variable.

Q: You think you have a 90% chance of passing your statistics class. This is an example of subjective probability.

Q: Two or more events are said to be exhaustive if one of them must occur.

Q: A random variable is a function that associates a numerical value with each possible outcome of a random phenomenon.

Q: If A and B are independent events with P(A) = 0.40 and P(B) = 0.50, then P(A/B) is 0.50.

Q: If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is a. .80 b. .40 c. .32 d. 1.20

Q: If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then the probability that either A or B or both occur is: a. 0.10 b. 0.12 c. 0.70 d. None of the above

Q: The joint probabilities shown in a table with two rows, and and two columns, and , are as follows: P( and ) = .10, P( and ) = .30, P( and ) = .05, and P(and ) = .55. Then P(|), calculated up to two decimals, is a. .33 b. .35 c. .65 d. .67

Q: Which of the following best describes the concept of marginal probability? a. It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs. b. It is a measure of the likelihood that a particular event will occur, given that another event has already occurred. c. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of the above.

Q: If A and B are any two events with P(A) = .8 and P(B|) = .7, then P(and B) is a. .56 b. .14 c. .24 d. None of the above

Q: If two events are independent, what is the probability that they both occur? a. 0 b. 0.50 c. 1.00 d. Cannot be determined from the information given

Q: If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is: a. 0.25 b. 0.40 c. 0.90 d. Cannot be determined from the information given

Q: There are two types of random variables, they are a. discrete and continuous b. exhaustive and mutually exclusive c. complementary and cumulative d. real and unreal

Q: If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a. 0.00 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

Q: If two events are mutually exclusive, what is the probability that both occur at the same time? a. 0.00 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

Q: If two events are mutually exclusive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

Q: The joint probabilities shown in a table with two rows, and and two columns, and , are as follows: P( and ) = .10, P( and ) = .30, P( and ) = .05, and P(and ) = .55. Then P(|), calculated up to two decimals, is a. .33 b. .35 c. .65 d. .67