1)

On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below.

x0 1 2 3 4 5 P(x).03 .32 .27 .19 .10 .09 total 1.00

(a)Calculate the mean and standard deviation.(Round your mean value to 2 decimal places and standard deviation to 3 decimal places.)

MeanStandard deviation

2)

Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 6 weeks with no radios sold, 22 weeks with one radio sold, 24 weeks with two radios sold, 34 weeks with three radios sold, 9 weeks with four radios sold, and 5 weeks with five radios sold. Calculate _x, _x², and _x, ofx,the number of ClearTone-400 radios sold at Sound City during a week using the estimated probability distribution.(Round your answers to 2 decimal places.)

3)

Calculate each binomial probability:

(a)X= 3,n= 5,

= .30(Round your answer to 4 decimal places.)

P(X= 3)

(b)X= 2,n= 8,

= .20(Round your answer to 4 decimal places.)

P(X= 2)

(c)X= 5,n= 15,

= .40(Round your answer to 4 decimal places.)

P(X= 5)

4)-

Calculate each binomial probability:

(a)Fewer than 2 successes in 13 trials with a 2 percent chance of success.(Round your answer to 4 decimal places.)

Probability

(b)At least 4 successes in 6 trials with a 30 percent chance of success.(Round your answer to 4 decimal places.)

Probability

(c)At most 8 successes in 19 trials with a 70 percent chance of success.(Round your answer to 4 decimal places.)

Probability

5)-

Historically, 7 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database.

The number of customers out of 14 who have an incorrect address in the database is a binomial random variable withn= 14 and

= .07.

(a)What is the probability that none of the next 14 repeat customers who call will have an incorrect address?(Round your answer to 4 decimal places.)

Probability

(b)What is the probability that three customers who call will have an incorrect address?(Round your answer to 4 decimal places.)

Probability

(c)What is the probability that four customers who call will have an incorrect address?(Round your answer to 4 decimal places.)

Probability

(d)What is the probability that fewer than five customers who call will have an incorrect address?(Round your answer to 4 decimal places.)

Probability

6)-

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .47.

a.Find the probability that in a sample of 11 customers, none of the 11 will order a nonalcoholic beverage.(Round your answer to 4 decimal places.)

Probability

b.Find the probability that in a sample of 11 customers, at least 4 will order a nonalcoholic beverage.(Round your answer to 4 decimal places.)

Probability

c.Find the probability that in a sample of 11 customers, fewer than 5 will order a nonalcoholic beverage.(Round your answer to 4 decimal places.)

Probability

d.Find the probability that in a sample of 11 customers, all 11 will order a nonalcoholic beverage.(Round your answer to 4 decimal places.)

Probability

7)-

Calculate each Poisson probability:

a.P(X= 4),= 3(Round your answer to 4 decimal places.)

Probability

b.P(X= 11),= 11(Round your answer to 4 decimal places.)

Probability

c.P(X= 6),= 5(Round your answer to 4 decimal places.)

Probability

7)-

According to J.D. Power and Associates' 2006 Initial Quality Study, consumers reported on average 0.8 problems per vehicle with new 2006 Volkswagens. In a randomly selected new Volkswagen,

(a)Find the probability of at least one problem.(Round your answer to 4 decimal places.)

P(X 1)

(b)Find the probability of no problems.(Round your answer to 4 decimal places.)

P(X= 0)

(c)Find the probability of more than three problems.(Round your answer to 4 decimal places.)

P(X> 3)

8)-

When the number of trials,n, is large, binomial probability tables may not be available. Furthermore, if a computer is not available, hand calculations will be tedious. As an alternative, the Poisson distribution can be used to approximate the binomial distribution whennis large andpis small. Here the mean of the Poisson distribution is taken to be=np. That is, whennis large andpis small, we can use the Poisson formula with=npto calculate binomial probabilities; we will obtain results close to those we would obtain by using the binomial formula. A common rule is to use this approximation whenn/p 500.

To illustrate this approximation, in the movieComa, a young female intern at a Boston hospital was very upset when her friend, a young nurse, went into a coma during routine anesthesia at the hospital. Upon investigation, she found that 10 of the last 26,000 healthy patients at the hospital had gone into comas during routine anesthesias. When she confronted the hospital administrator with this fact and the fact that the national average was 7 out of 104,000 healthy patients going into comas during routine anesthesias, the administrator replied that 10 out of 26,000 was still quite small and thus not that unusual.

Note: It turned out that the hospital administrator was part of a conspiracy to sell body parts and was purposely putting healthy adults into comas during routine anesthesias. If the intern had taken a statistics course, she could have avoided a great deal of danger.)

(a)Use the Poisson distribution to approximate the probability that 10 or more of 26,000 healthy patients would slip into comas during routine anesthesias, if in fact the true average at the hospital was 7 in 104,000. Hint:=np= 26,000 (7/104,000) = 1.8.(Leave no cell blank. You must enter "0" for the answer to grade correctly. Do not round intermediate calculations. Round final answer to 5 decimal places.)

(b)Given the hospital's record and parta, what conclusion would you draw about the hospital's medical practices regarding anesthesia?

9)-

A rock concert promoter has scheduled an outdoor concert on July 4th. If it does not rain, the promoter will make $31,841. If it does rain, the promoter will lose $12,020 in guarantees made to the band and other expenses. The probability of rain on the 4th is .6.

(a)What is the promoter's expected profit? Is the expected profit a reasonable decision criterion?(Round your answers to 1 decimal place.)

(b)

How much should an insurance company charge to insure the promoter's full losses?(Round final answer to the nearest dollar amount.)