Exam 5: Discrete Probability Distributions

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. -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 gets audited at least once is ________.

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

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 standard deviation of the number of accidents is ________.

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 produced 4.0 bad bulbs.

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

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 total variance of value gain if you invest in both houses?

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, if you decide to choose Design A for half of the production lines and Design B for the other half, what is the coefficient of variation 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. -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?

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 ________.

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. -The probability of receiving a 911 call on a university campus is the same every day. The probability of having received a 911 call on a single day does not change the probability of receiving a 911 call on any other day. Which of the following distributions would you use to determine the probability that a 911 call will be received next day?

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. -Suppose that past history shows that 6% of college students prefer Brand A Cola. A sample of 10,000 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 Brand A cola?

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 fail 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. -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?

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. -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 variance of the number of times she will be audited 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 mean number of transactions per month for this subscriber?

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 5-6 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 produced between 5.0 and 8.0 inclusive bad bulbs.

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?