Exam 5: Some Important Discrete Probability Distributions

$\text { TABLE 5-3 }$ The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Table 5-3, the probability of at least one retransmission is____ .

A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution?

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

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 half of the production lines and Design B for the other half, what is your expected profit?

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 standard deviation of your profit when Design A is chosen?

TABLE 5-6 The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. -Referring to Table 5-6, what is the probability that any particular cookie being inspected has fewer than 5.0 chip parts.

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Probability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, if you can invest half 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?

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10.0 calls a day. The standard deviation of the number of 911 calls in a day is _____.

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?

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

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______

Referring to Table 5-8, what is your expected profit when Design A is chosen?

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 less than 2 prefer brand C is_______

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

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Prob ability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, what is the standard deviation of the value gain for the house in neighborhood B?

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, at least half of the cars have defective radios?

TABLE 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 double satellite media. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Table 5-3, the standard deviation of the number of retransmissions is____

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Probability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, if you can invest 30% 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 5-2 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 exactly 1 business succeeds is _____.

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Probability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, if your investment preference is to maximize your expected return while exposing yourself to the minimal amount of risk, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?