Exam 5: Discrete Probability Distributions

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 ________.

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 more than 4 consumers from Canada are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

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 ____________.

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

Current estimates suggest that 75% of the home-based computers in a foreign country have access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that more than 9 of those sampled currently do not have access to on-line services.

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 your expected profit when Design A is chosen?

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio- Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that The teacher on bus duty will likely be certified in CPR?

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 custoers, the chain will have at least one mishandled bags?

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 standard deviation of the value gain for the house in neighborhood B?

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

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The variance of the number of power outages 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 more than 4 consumers from the U.S. plan to spend more on holiday shopping 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?

SCENARIO 5-10 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 Scenario 5-10, what is probability that at least five security transactions will be conducted in one month?

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 at least two mishandled bags?

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 all 5 consumers from China are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

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 no more than 2 times 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 the U.S. are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

SCENARIO 5-2 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 -Referring to Scenario 5-2, the mean or expected value of the number of accidents 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 no mishandled bags?