Exam 5: Discrete Probability Distributions

In a Poisson distribution, the mean and variance are equal.

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

SCENARIO 5-12 Phone calls arrive at the rate of 50 per hour at the reservation desk for Queen City Airways.The desk manager has asked you for an analysis of the call rates and probabilities to better understand the operation and determine if more call desk workers are needed. -Using Scenario 5-12, What is the probability of receiving exactly 10 calls in a 12-minute period?

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that more than 3 prefer brand C 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 once is .

SCENARIO 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 Scenario 5-11, what is mean number of transactions per month for this subscriber?

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 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent). -Referring to Scenario 5-2, the probability that exactly 1 business succeeds is .

Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will have at least one mishandled bag? -Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than ten mishandled bags?

SCENARIO 5-4 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 5-4, the probability of 3 accidents is .

In a binomial distribution

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.

Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will have at least one mishandled bag? -Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than five but less than eight mishandled bags?

SCENARIO 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 Scenario 5-11, what is probability that no security transaction will be conducted in one month?

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

Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will have at least one mishandled bag? -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?

If n = 10 and $\pi = 0.70$ , then the standard deviation of the binomial distribution is

Suppose that 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 .

SCENARIO 5-5 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 5-6, what is the probability that any shift being inspected has produced fewer than 5.0 bad bulbs.

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?