Exam 5: Discrete Distributions

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______

For the Poisson distribution the mean and the variance are the same.

The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A batch contains two defective boards; and x is the number of defective boards in the sample.P(x=1)is _______.

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_______________.

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0)is ______________.

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 following graph is a binomial distribution with n = 6. This graph reveals that ____________.

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, 2016.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 5 cars arriving over a five-minute interval is _______.

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2)is ______________.

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 _______.

For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

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.

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, 15 invoices are sampled at random.The mean (average)value of the number of the 15 sampled invoices that receive discount is _______

If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?

If sampling is performed without replacement, the hypergeometric distribution should be used.However, the binomial may be used to approximate this if _______.

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution, x represents the number of evenings the family dines outside their home during a week. x P(x) 0 0.30 1 0.50 2 0.10 3 0.10 The standard deviation of x is _______________.