Exam 5: Discrete Probability Distributions

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 less than two and more than eight mishandled bags?

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,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?

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 no mishandled bags?

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.

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 bags?

The diameters of 10 randomly selected bolts have a binomial distribution.

If n = 10 and π = 0.70,then the standard deviation of the binomial distribution is

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 probability that more than two security transactions will be conducted in one month?

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?

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 your expected profit when Design A is chosen?

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,if you decide to choose Design A for 30% of the production lines and Design B for the remaining production lines,what is the expected profit?

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 ________.

The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.

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,no more than half of the cars have defective radios?

TABLE 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town.This year,there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Table 5-10,what is the probability that none of the new employees will be from University B?

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 expected profit if you increase the shift of your production lines and choose to produce both designs?

TABLE 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently. -Referring to Table 5-1,the probability that both sound an alarm in the presence of smoke is ________.

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis,Oregon. -Referring to Table 5-4,the variance of the number of accidents is ________.

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis,Oregon. -Referring to Table 5-4,the mean or expected value of the number of accidents is ________.

The variance of the sum of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.