Exam 5: 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.When there are 8 local letters mailed,what is the probability that the number delivered will be within 2 standard deviations of the mean?

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

The number of ways to arrange x successes among n trials is equal to:

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

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.

According to data from the state blood program,40 percent of all individuals have group A blood.Suppose that of six randomly selected individuals,three have group A blood.Would you believe the data from the state blood program?

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?

In a hypergeometric probability distribution of a population of N items,r refers to the number of successes and N - r to the number of failures.

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?

The mean of the binomial distribution is equal to:

X has the following probability distribution P(X): Compute the expected value of X.

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

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 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?

According to data from the state blood program,40 percent of all individuals have group A blood.If six individuals give blood,find the probability that at least 3 of the individuals have group A blood.

An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year.Suppose that the probability that the Hummer will be stolen is 0.0075.Calculate the expected net profit for the insurance company.

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

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

Historical data for a local steel manufacturing company show that the average number of defects per standard sheet of steel 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 sheets of metal.

For a discrete probability distribution,the value of p(x)for each value of x falls between -1 and 1.

A vaccine is 95 percent effective.What is the probability that it is not effective for more than one out of 20 individuals?