Exam 5: Discrete Probability Distributions

A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). Which of the following distributions would you use to determine the probability that all of them will fail?

TABLE 5-2 A certain type of new business succeeds 60% of the time. Suppose that three 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 at least one business succeeds is ________.

TABLE 5-2 A certain type of new business succeeds 60% of the time. Suppose that three 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 three businesses succeed is ________.

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month. Also the number of small businesses that declared bankruptcy was the same every month. Which of the following distributions would you use to determine the probability that more than three bankruptcies will occur next month?

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 5-3 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. -Referring to Table 5-3, the mean or expected value for the number of retransmissions is ________.

TABLE 5-7 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 5-7, what is the variance of your profit when Design A is chosen?

TABLE 5-7 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 5-7, what is the variance of your profit when Design B 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 variance of the number that prefer Brand C is ________.

TABLE 5-6 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 5-6, what is the expected value gain for the house in neighborhood A?

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day. The probability of seven or eight 911 calls in a day is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The average number that you would expect to prefer Brand C is ________.

TABLE 5-6 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 5-6, what is the standard deviation of the value gain for the house in neighborhood B?

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

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 at least 1 prefers Brand C is ________.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have five such alarms in your home and they operate independently. Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

A national trend predicts that women will account for half of all business travelers in the next three years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

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 5-3 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 5-8 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 5-8, 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?