Question

A tire manufacturer would like to estimate the average tire life of its new? all-season light...

A tire manufacturer would like to estimate the average tire life of its new? all-season light truck tire in terms of how many miles it lasts. Determine the sample size needed to construct a 97?% confidence interval with a margin of error equal to 2 comma 800 miles. Assume the standard deviation for the tire life of this particular brand is 7 comma 000 miles.
The sample size ne

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

standard deviation = = 7,000

margin of error = E =2,800

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.170

Sample size = n = ((Z/2 * ) / E)2

= ((2.170 * 7,000) / 2800)2

= 29.4306 = 29

Sample size = 29

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