Exam 5: Discrete Probability Distributions

On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store.What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?

In a binomial distribution

SCENARIO 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and Design B for the other half, what is your expected profit?

SCENARIO 5-5 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, none of the cars have defective radios?

SCENARIO 5-12 Phone calls arrive at the rate of 50 per hour at the reservation desk for Queen City Airways.The desk manager has asked you for an analysis of the call rates and probabilities to better understand the operation and determine if more call desk workers are needed. -Using Scenario 5-12, What is the expected number of calls when calculating the probability of receiving nine calls in a 12-minute period?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students.Ten of the 15 students have no prior competition experience while the others have some degree of experience.What is the probability that at least 1 of the members chosen for the team have some prior competition experience?

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

Which of the following about the binomial distribution is not a true statement?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month.Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Scenario 5-11, what is probability that no more than five security transactions will be conducted in one month?

SCENARIO 5-5 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, no more than half of the cars have defective radios?

SCENARIO 5-13 Bell Computers manufactures personal computers at two plants, one in Arkansas and one in Utah.The Arkansas plant has 50 employees; the Utah one has 40 employees.A random sample of 12 employees was selected to complete a job satisfaction questionnaire -Using Scenario 5-13, what is the probability at least three of the employees completing the questionnaire are from the Arkansas plant?

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The mean number that you would expect to prefer brand C is ________.

SCENARIO 5-3 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network. -Referring to Scenario 5-3, the standard deviation of the number of retransmissions is ________.

Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time.In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

If the covariance between two investments is zero, the variance of the sum of the two investments will be equal to the sum of the variances of the investments.

SCENARIO 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers.In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than five but less than eight mishandled bags?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, what is the covariance of the two houses?

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that at least 1 prefers brand C is ________.

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.