Exam 6: Discrete Probability Distributions

Which of the following statements are true?

Students Students use the university mainframe computer log-on during their designated time periods.Assume that the number of students logging on each five-minute interval is 12.5,and these log-on attempts are Poisson distributed. -Find the probability that exactly 9 students will log-in during the next 5-minute interval.

The ____________________ probability distribution deals with consecutive trials that are statistically independent,each of which has only two possible outcomes,generally referred to as success or failure.

One characteristic of a discrete probability distribution is that values of x are exhaustive.

MBI Co. The MBI Company found that at the end of each month,2% of its two million accounting entries contained errors.Today,one operator has made 50 computer entries. Determine the mean and standard deviation of errors in accounting entries. Mean = ____________________ SD = ____________________

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 3 girls will be selected?

Canoe club A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate. -What is the probability that four of the five canoes will capsize?

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that at least 5 Democrats will be selected for the committee?

The variance of a binomial distribution for which n = 75 and = 0.20 is:

An EMS service averages 5.2 calls per 8-hour shift.During a shift in which 8 or more calls occur,the EMS crew receives one extra hour pay.If the hourly wage is $15 for each 8-hour day,and taking into account the extra-effort days,what is the average wage for an 8-hour day?

Students Students use the university mainframe computer log-on during their designated time periods.Assume that the number of students logging on each five-minute interval is 12.5,and these log-on attempts are Poisson distributed. -Find the probability that between 8 and 10 (inclusive)students will log-in during the next 5-minute interval.

Which of the following is not a characteristic of the hypergeometric distribution?

Fishing During the peak fishing months,a marina at a large man-made reservoir noted that boats were arriving at the average of 3.2 boats every twenty minutes to use the boat ramp.Let x be the number of boats arriving during the next twenty minutes. -What is the probability that during the next twenty minutes the number of boats arriving to load or unload is at least one?

Stockholders The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected. -What is the probability that at least one is a homemaker?

A fast food hamburger restaurant manager is interviewing high school persons age sixteen for possible employment.Persons age sixteen who apply for jobs in the area have no prior work-for-pay experience ninety percent of the time.Let x be the number of the four high school persons age sixteen who have no prior work-for-pay experience.If the manager plans to hire four,what is the probability that two of the four will have work experience?

Canoe club A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate. -What is the probability that less than two of the five canoes will capsize?

Distribution The probability distribution of a discrete random variable x is shown below. x 0 1 2 3 p(x) .25 .40 .20 .15 -Find the expected value,the variance,and the standard deviation of x. E(x)= ____________________. Variance = ____________________. SD = ____________________.

Fans Fans arriving on a given Saturday night for a non-conference home basketball game average 0.25 per second.Let x represent the number of fans arriving at a specified time period. -What is the probability that thirty or more fans arrive between 7:15 and 7:16 P.M.?

Theoretically,the number of times an event can occur over the given time span in a Poisson distribution has no limit.

Chamber of Commerce A local chamber of commerce is backing a plan for a new convention center.The chamber states that 60 percent of the voters favor the plan,which would raise tourism business and taxes for the residents.Four of the registered voters in the community are called at random.X is the number of voters called who say they favor the plan. -Find the probability that no one says they favor the plan.