Exam 5: Discrete Probability Distributions

If n = 10 and π = 0.70, then the standard deviation of the binomial distribution 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 probability that fewer than 2 prefer brand C is ________.

A national trend predicts that women will account for half of all business travelers in the next 3 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 at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

SCENARIO 5-8 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 mean number of bad bulbs per shift is 6.0. -Referring to Scenario 5-8, what is the probability that any particular shift being inspected has produced 4.0 bad bulbs.

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 ________.

Another name for the mean of a probability distribution is its expected value.

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

SCENARIO 5-6 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 Scenario 5-6, the probability that at least 1 business succeeds is ________.

The number of 911 calls in a small city 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 ____________.

SCENARIO 5-7 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Suppose you randomly select 5 consumers from each of the three countries. -Referring to Scenario 5-7, the probability that no more than 2 consumers from Canada are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

SCENARIO 5-3 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 Scenario 5-3, what is the expected value gain for the house in neighborhood B?

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 at least 3 power outages in a year is ____________.

SCENARIO 5-7 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Suppose you randomly select 5 consumers from each of the three countries. -Referring to Scenario 5-7, the probability that no more than 2 consumers from China are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

SCENARIO 5-4 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 Scenario 5-4, 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 ________.

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 exactly 3 prefer brand C is ________.

SCENARIO 5-4 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 Scenario 5-4, what is the variance of your profit when Design A is chosen?

SCENARIO 5-7 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Suppose you randomly select 5 consumers from each of the three countries. -Referring to Scenario 5-7, the probability that none of the 5 consumers from Canada are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

SCENARIO 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 Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than eight mishandled bags?

SCENARIO 5-8 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 mean number of bad bulbs per shift is 6.0. -Referring to Scenario 5-8, what is the probability that any particular shift being inspected has produced fewer than 5.0 bad bulbs.