# Until this year, the mean braking distance of a Nikton automobil

May 5th, 2015
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Until this year, the mean braking distance of a Nikton automobile moving at 60 mi per hour was 175 ft. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 81 cars and determine the sample mean braking distance. The results are the following. Sample Size = 81 Sample Mean = 167 ft Sample Standard Deviation = 27 ft a. Compute the 95% confidence interval for the mean braking distance. b. Interpret this interval. c. How many cars should be tested if Nikton wants to be 95% confident of being within 2 ft of the population mean braking distance?

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Solution a) given alpha=0.05formula usedconfodence interval= [ 81 - z(alpha)/2]*(27/81) ,81 - z(alpha)/2]*(27/81)]so by putting valuesxbar+/- Z*s/vn--> 167 +/- 1.96*27/sqrt(81)--> (161.12, 172.88)b) it is seen from the data that we have 95% confident that the population mean will be within this interval because this means that if you take 100 samples of size 81 in 95% case the sample mean will fall in this intervalc) let n=required sample size,alpha=0.05[z(alpha)/2]*(27/n) = 2 (by the question)z(alpha)/2 can be found from normal table .putting valuesn=(Z*s/E)^2=(1.96*27/2

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