8% of vehicles of a particular brand historically have required warranty service

Question

8% of vehicles of a particular brand historically have required warranty service during the first year of ownership. Suppose that a random sample of 150 vehicles of this brand is considered. Use the normal approximation to the binomial distribution to answer the following questions.

a. What is the probability that more than 20 of these vehicles will require warranty service during the first year of ownership? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability =

b. What is the probability that 10 or fewer of these vehicles will require warranty service during the first year of ownership? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability =

c. What is the probability that between 16 and 20 of these vehicles (inclusive) will require warranty service during the first year of ownership? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability =

Explanation / Answer

Here p=0.08 and n=150

This is binomial distribution so mean=np=12 and sd=sqrt(NPR)=3.32

a. We need to find P((x>20)=P(z>(20-12)/3.32)=P(z>2.41)=0.008

b. P(x<10)=P(z<(10-12)3.32)=P(z<-0.60)=0.2743

c. P(16<x<20)=P(1.20<z<2.41)=0.1071

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