Exam 5: Discrete Probability Distributions

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 standard deviation of the number of accidents 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 _.

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 .

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 .

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 .

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 at least two mishandled bags?

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?

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

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 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 .

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 exactly 4 prefer brand C 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.

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 at least 6.0 bad bulbs.

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

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 _.

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

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? 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 or at least eight mishandled bags?