Exam 6: Discrete Random Variables

A discrete probability distribution is expressed as a table, graph, or ________ that gives the probability associated with each possible value that the random variable can assume.

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, find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

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

A lawyer believes that the probability is .3 that she can win a discrimination suit. If she wins the case, she will make $400,000; but if she loses, she gets nothing. Assume that she has to spend $75,000 preparing the case. What is her expected gain?

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

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 standard deviation of the random variable x?

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 fewer than two troubles will be repaired on the same day?

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

Determine the probability that a 3 will appear twice, if a single fair die is rolled 10 times.

The variable Home Ownership can take on one of two values: 1 if the person living in the home owns the home and 0 if the person living in the home does not own the home. This is an example of a discrete random variable.

Which one of the following statements is not an assumption of the binomial distribution?

A fair die is rolled 10 times. What is the average number of even number outcomes?

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X > 4).

Of all individual tax returns, 37 percent include errors made by the taxpayer. If IRS examiners are assigned randomly selected returns in batches of 12, find the mean and standard deviation for the number of erroneous returns per batch.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 3 customers arriving within a minute.

The internal auditor for your company believes that 10 percent of your invoices contain errors. To check this theory, 20 invoices are randomly selected, and 5 are found to have errors. What is the probability that of the 20 invoices selected, 5 or more would contain errors if the theory is valid?

According to a survey of adults, 64 percent have money in a bank savings account. If we were to survey 50 randomly selected adults, find the mean number of adults who would have bank savings accounts.

Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the standard deviation of X.

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.

The probability distribution of X is What is the variance of X?