Exam 5: Discrete Probability Distributions

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 _.

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 .

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

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be exactly 3 power outages in a year 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? ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: 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 5-3 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Scenario 5-3, the standard deviation of the number of retransmissions is _.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week.Interpret this value.

SCENARIO 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 network. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is_.

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 at least 1 accident is .

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?

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 all the hotels in the sample offered hairdryers in the bathrooms.

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = .

What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem?The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.When the production process is in control, the mean number of blue chocolate chips per bagis 6.0.The manager is interested in analyzing the probability that any bag being inspected has fewer than 5.0 blue chocolate chips.

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? ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: 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 or more than eight mishandled bags?

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? ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: 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 four mishandled bags?

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? ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: 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 5-2 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 all 3 businesses fail is _.

The largest value that a Poisson random variable X can have is n.

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 expected number of calls when calculating the probability of receiving nine calls in a 12-minute period?

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem?An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims.It is known that the industry proportion for false claims is 3%.The consulting firm has decided to randomly and independently sample100 of the company's insurance claims.They believe the number of these 100 that are false will yield the information the company desires.