Exam 7: Discrete Probability Distributions

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The standard deviation of x is ___.

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x > 0) is ___.

The number of successes in a hypergeometric distribution is unknown.

Twenty-five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they made a purchase during their visit. Each of the shoppers has the same probability of answering 'yes' to having made a purchase. The probability that exactly four of the twenty-five shoppers made a purchase could best be found by ___.

Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes. The number of occurrences per hour follows a Poisson distribution with λ equal to ___.

In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent.

Which of the following random variables is geometric?

A Poisson distribution is characterized by one parameter.

A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors, the mean value of x is ___.

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 3 cars arriving over a five-minute interval is ___.

The probability that a student will pass an exam on any trial is 0.7. What is the standard deviation of the number of trials needed to pass the exam?

During a recent sporting event, a quarter is tossed to determine which team picks the starting side. Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls 'heads', what is the probability that exactly two heads are observed in three tosses?

The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems.

A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately ___.

The probability that a student will pass an exam on any trial is 0.7. What is the expected number of trials needed to pass the exam?

The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month: The standard deviation of this distribution is ___.

One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, x has a ___ distribution.

One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, x has a ___.

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The mean (average) value of x is ___.