Exam 6: Discrete Random Variables

The random variable x has a hypergeometric distribution and the population contains 12 items. If you wanted to find the number of defects in a random sample of 3 selected items when the population contains 5 defects, identify the N, n, and r.

An insurance company will insure a $75,000 particular automobile make and model for its full value against theft at a premium of $1500 per year. Suppose that the probability that this particular make and model will be stolen is .0075. Find the premium that the insurance company should charge if it wants its expected net profit to be $2000.

The probability distribution of X is What is the expected value of X?

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the standard deviation for this distribution?

Which of the following statements about the binomial distribution is not correct?

Two characteristics, or assumptions, of the Poisson distribution are that

An important part of the customer service responsibilities of a cable company is the speed with which service troubles can be repaired. Historically, the data show that the likelihood is .75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, find the mean number of troubles repaired on the same day.

If p = .1 and n = 5, then the corresponding binomial distribution is ________.

The internal auditor for your company believes that 10 percent of their invoices contain errors. To check this theory, 20 invoices are randomly selected and 5 are found to have errors. Based on the above information, the claim of the auditor will be rejected.

An important part of the customer service responsibilities of a cable company is the speed with which service troubles can be repaired. Historically, the data show that the likelihood is .75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day?

During off-hours, cars arrive at a tollbooth on the East-West toll road at an average rate of .5 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next minute, three cars will arrive?

The equation for the variance of the binomial distribution is given by

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the standard deviation.

The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and is such that the probability of success on any trial is the same.

According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the mean number of individuals having group A blood.

If x is a binomial random variable, then the standard deviation of x is given by

A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, calculate the probability that exactly 4 of the jobs were not completed within the bid time.

The number of calls coming into a call center follows a Poisson distribution with a mean of 120 calls per hour. What is the probability of no calls in a one-minute interval?

During off-hours, cars arrive at a tollbooth on the East-West toll road at an average rate of .5 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next five minutes, three cars will arrive?

If the number of surface nonconformities on a specific size of metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defects is given most likely by ________ distribution(s).