Exam 5: Discrete Probability Distributions

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 _.

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 three calls in a 6-minute period?

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 neither sound an alarm in the presence of smoke is_.

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_.

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

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that exactly 5 bankruptcies occur next month.

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 at least 1 prefers brand C is .

The connotation "expected value" or "expected gain" from playing roulette at a casino means

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 four mishandled bags?

If the outcomes of a variable follow a Poisson distribution, then them

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? -Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have between two and four inclusive mishandled bags?

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 5-11 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 variance of the number of transactions per month for this subscriber?

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.The probability of seven or eight 911 calls in a day 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 expected number of times she will be audited 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 exactly 3 power outages in a year 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 between 5.0 and 8.0 inclusive bad bulbs.

The number of 911 calls in a small city has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 911 calls in a day is .

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that more than 3 bankruptcies occur next month.