Question

a) Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area to the right of z = 1.51 is ____

b) The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.5 minutes and a standard deviation of 2.1 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes


(b) longer than 5 minutes


(c) between 8 and 15 minutes

c) A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean μ = 38 minutes and standard deviation σ = 5 minutes.

(a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (Round your answer to four decimal places.)


(b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (Round your answer to four decimal places.)


(c) Comment on the differences of the results in parts (a) and (b).

The probability in part (b) is  ---Select--- the same as larger than smaller than part (a) because the  ---Select--- mean standard deviation is  ---Select--- smaller larger for the x distribution.

d) According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation?
%

Within 2 standard deviations?
%

Within 3 standard deviations?
%

e) Can a normal distribution always be used to approximate a binomial distribution? Explain your answer.

a, No. For the approximation to be accurate, np > 5 and nq < 5.

b. No. For the approximation to be accurate, np > 5 and nq > 5.    

c. No. For the approximation to be accurate, np > 10 and nq > 10.

d. Yes. We can always use the normal distribution to approximate the binomial distribution.

Answer 1

(1)

P(Z > 1.51)=1-P(Z < 1.51)=1-0.9345 = 0.0655

(2)

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