Exam 5: Discrete Probability Distributions

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, the table above is called the ______________ for the two designs.

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 no more than 1 power outage in a year is ____________.

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 mean number of transactions per month for this subscriber?

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 more than two and at least eight 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 less than 4 consumers from Canada plan to spend more on holiday shopping 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 at least 3 consumers from the U.S. 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 at least once 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 expected number of times she will be audited 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 variance of the number of accidents 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 2 or fewer prefer 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 less than 4 consumers from China plan to spend more on holiday shopping is ________.

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day. The probability of 2 or more 911 calls in a day 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 less than two and more than eight mishandled bags?

SCENARIO 5-5 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently. -Referring to Scenario 5-5, the probability that at least one sounds an alarm in the presence of smoke is ________.

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that exactly 6 tickets are written on a randomly selected day from this population.

If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .

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 between two and four inclusive 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 the U.S. are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

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 variance of the number of transactions per month for this subscriber?

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 exactly 1 business succeeds is ________.