Exam 5: Discrete Probability Distributions

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 eight mishandled bags?

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 4.0 bad bulbs.

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 mean or expected value of the number of accidents 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 at least one sounds an alarm in the presence of smoke is _.

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

If n = 10 and $\pi = 0.70$ , then the mean of the binomial distribution 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 no more than two or at least eight mishandled bags?

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 1 power outage in a year 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 _.

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 fewer than 2 prefer brand C 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 all 3 businesses succeed 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 probability that no more than five security transactions will be conducted in one month?

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 variance of the number of accidents 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 less than 5.0 or more than 8.0 bad bulbs.

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 1 prefers brand C 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 2 or fewer prefer brand C 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 4 prefer brand C is .

If $\pi$ remains constant in a binomial distribution, an increase in n will not change the mean.

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.

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