Exam 5: Discrete Probability Distributions

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.

A probability distribution is an equation that

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who has not studied for the test decides to answer all questions randomly.What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?

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 less than two or more than 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 variance for the number of retransmissions is _.

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

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 between 1 and 3 inclusive power outages in a year is _.

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 exactly 3 prefer brand C is .

SCENARIO 5-1 The probability that a 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 5-1, the probability that both sound an alarm in the presence of smoke 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 fewer than six 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 at least 1 business succeeds is .

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 at least 3 power outages in a year 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 less than 6 tickets are written on a randomly selected day from this population.

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.

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 at least two mishandled bags?

The Poisson distribution can be used to model a continuous random variable.

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 probability of no retransmissions is .

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?

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 .

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 eight mishandled bags?