Exam 5: Discrete Probability Distributions

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?

If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2)= ________.

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. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -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 5-10 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 at least one of the new employees will be from University A?

In a binomial distribution

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 5-8 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. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -Referring to Table 5-8, if your investment preference is to maximize your expected profit and not worry at all about the risk that you have to take, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

In a Poisson distribution, the mean and standard deviation are equal.

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 two of the new employees will be from University A?

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 at least five security transactions will be conducted in one month?

In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she does not get audited is ________.

The covariance between two investments is equal to the sum of the variances of the investments.

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly 3 power outages in a year 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 hotel chain will have no more than four mishandled bags?

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 binomial 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. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -Referring to Table 5-8, what is the total standard deviation of the profit if you increase the shift of your production lines and choose to produce both designs?

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 all of the new employees will be from University B?

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 A?