Exam 6: Discrete Random Variables

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the average number you expect to be delivered the next day?

The binomial distribution is characterized by situations that are analogous to

The mean of a hypergeometric random variable is defined as

The requirement that the probability of success remains constant from trial to trial is a property of the ________ distribution.

The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, no more than 2 customers use the service desk?

A test has 6 multiple-choice questions, each with 4 choices. What is the probability of guessing 5 or more questions correctly?

An appliance manufacturer gives a warranty and 95 percent of its appliances do not require repair before the warranty expires. An organization buys 10 of these appliances. Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. Determine the standard deviation of the number of defects for 32 units.

Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the standard deviation of the distribution.

The requirement that the probability of success remains constant from trial to trial is a property of the ________ distribution.

If the population size is at least 20 times larger than the sample size, a hypergeometric distribution can be approximated by the binomial distribution.

A multiple-choice test has 30 questions and each one has five possible answers, of which only one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.

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 mean number of jobs completed within the bid time.

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the mean of the random variable x?

The yearly proportional return for stock G = x, the yearly proportional return for stock H = y, μ_x = .16, μ_y = .07, σ_x = .11, σ_y = .11, and σ_xy² = .0321. Find the mean and standard deviation of the portfolio return: P = .5x + .5y.

If x is a Poisson random variable with a mean of 10, what is the probability that x is greater than or equal to 2?

The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, exactly 2 customers use the service desk?

With two random variables x and y, a positive covariance says that as x increases, y tends to increase in a linear fashion.

Assume the number of trucks passing an intersection has a Poisson distribution with a mean of 5 trucks per minute. What is the probability of 0 or 1 trucks in one minute?

The mean of the binomial distribution is equal to