Exam 5: Discrete Probability Distributions

The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is 0.002.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at most 5,000 of them will malfunction in case of a fire?

Suppose that past history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 4 prefer brand C is ________.

TABLE 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 Table 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?

TABLE 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 Table 5-11,what is the probability that at least five security transactions will be conducted in one month?

True or False: 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.

TABLE 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 Table 5-8,what is the standard deviation of your profit when Design B is chosen?

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 no more than 1 of the members chosen for the team have some prior competition experience?

Suppose that past history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that more than 3 prefer brand C is ________.

True or False: The variance of the sum of two investments will be equal to the sum of the variances of the two investments when the covariance between the investments is zero.

TABLE 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent). -Referring to Table 5-2,the probability that all 3 businesses succeed is ________.

TABLE 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 Table 5-9,what is the probability that in the next 1,000 customers,the chain will have at least one mishandled bag?

TABLE 5-6 The quality control manager of Green Bulbs Inc.is inspecting a batch of energy saving compact fluorescent light bulbs.When the production process is in control,the average number of bad bulbs per shift is 6.0. -Referring to Table 5-6,what is the probability that any particular shift being inspected has less than 5.0 or more than 8.0 bad bulbs?

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

TABLE 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 Table 5-7,what is the standard deviation of the value gain for the house in neighborhood A?

TABLE 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 Table 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have fewer than six mishandled bags?

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 exactly half of the members chosen for the team have some prior competition experience?

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days.In reality,the prices of only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from the list,he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20% after 30 days?

The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.When the production process is in control,the average number of blue chocolate chips per bag is 6.0.Suppose that the probability of a blue chocolate chip in a bag is constant across bags and the number of blue chocolate chips in one bag is independent of the number in any other bag.Which of the following distributions would you use to figure out the probability that any particular bag being inspected has 4.0 blue chocolate chips?

What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that exactly 5 bankruptcies occur next month.