Exam 6: Discrete Probability Distributions

A help desk receives an average of four calls per hour on its toll-free number. For any given hour, find theprobability that it will receive exactly six calls. Use the Poisson distribution.

In a lottery, a player must choose 6 numbers between 1 and 48 inclusive. Six balls are then randomly selectedfrom an urn containing 48 balls numbered from 1 to 48. The random variable X represents the number ofmatching numbers. What are the mean and standard deviation of the random variable X?

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poissondistribution with a mean of 7.2. Find the probability that less than three accidents will occur next month on thisstretch of road.

Provide an appropriate response. -The random variable x represents the number of credit cards that students have along with the correspondingprobabilities. Graph the probability histogram. () 0 0.49 1 0.05 2 0.32 3 0.07 4 0.07

Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Find the probability of exactly nine girls in ten births.

A manager at a local company asked his employees how many times they had given blood in the last year. Theresults of the survey are given below. The random variable x represents the number of times a person gaveblood and P(x) represents the probability of selecting an employee who had given blood that percent of thetime. What is the standard deviation for the number of times a person gave blood based on this survey? x 0 1 2 3 4 5 6 P(x) 0.30 0.25 0.20 0.12 0.07 0.04 0.02

In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizensare chosen, what is the standard deviation of the number favoring the health center?

Given that a random variable x, the number of successes, follows a Poisson process, the probability of 2 or moresuccesses in any sufficiently small subinterval is

The probability that a house in an urban area will develop a leak is 5%. If 20 houses are randomly selected,what is the mean of the number of houses that developed leaks?

The random variable x represents the number of tests that a patient entering a clinic will have along with thecorresponding probabilities. Find the mean and standard deviation for the random variable x. () 0 1 2 3 4

A legendary football coach was known for his winning seasons. He consistently won nine or more games perseason. Suppose x equals the number of games won up to the halfway mark (six games) in a 12-game season. Ifthis coach and his team had a probability p = 0.75 of winning any one game (and the winning or losing of onegame was independent of another), then the probability distribution of the number x of winning games in aseries of six games is: x P(x) 0 0.000244 1 0.004395 2 0.032959 3 0.131836 4 0.296631 5 0.355957 6 0.177979 Find the expected number of winning games in the first half of the season for this coachʹs football teams.

An Apple Pie Company knows that the number of pies sold each day varies from day to day. The ownerbelieves that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pieseach day at a cost of $2 each. Assume any pies that go unsold are thrown out at the end of the day. If she sellsthe pies for $4 each, find the probability distribution for her daily profit.

According to insurance records, a car with a certain protection system will be recovered 92% of the time. If 800stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recoveredafter being stolen?

Suppose x is a random variable for which a Poisson probability distribution with λ = 8.7 provides a goodcharacterization. Find μ for x.

Given that a random variable x, the number of successes, follows a Poisson process, then the probability ofsuccess for any two intervals of the same size

Provide an appropriate response. -The number of violent crimes committed in a day possesses a distribution with a mean of 1.8 crimes per dayand a standard deviation of four crimes per day. A random sample of 80 days was observed, and the samplemean number of crimes for the sample was calculated. The data that was collected in this experiment could bemeasured with a __________ random variable.

A customer service firm receives an average of three calls per hour on its toll-free number. For any given hour,find the probability that it will receive at least three calls. Use the Poisson distribution.

Provide an appropriate response. -The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings.Management at the home improvement store randomly selected 35 customers last Saturday morning anddecided to observe their shopping habits. They recorded the number of items that each of the customerspurchased as well as the total time the customers spent in the store. Identify the types of variables recorded bythe home improvement store.

A IRS auditor randomly selects 3 tax returns from 42 returns of which 15 contain errors. What is the probabilitythat none of the returns she selects contains an error?

If p is the probability of success of a binomial experiment, then the probability of failure is