Question

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 14 years with a variance of 25. If the claim is true, in a sample of 50 wall clocks, what is the probability that the mean clock life would differ from the population mean by greater than 1.5 years

Answer 1

The probability that the mean clock life would differ from the population mean by greater than 12.5 years is 98.30%.

Given mean of 14 years, variance of 25 and sample size is 50.

We have to calculate the probability that the mean clock life would differ from the population mean by greater than 1.5 years.

μ=14,

σ=$\sqrt{25}$=5

n=50

s orσ =5/$\sqrt{50}$=0.7071.

This is 1 subtracted by the  p value of z when X=12.5.

So,

z=X-μ/σ

=12.5-14/0.7071

=-2.12

P value=0.0170

1-0.0170=0.9830

=98.30%

Hence the probability that the mean clock life would differ from the population mean by greater than 1.5 years is 98.30%.

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There is a mistake in question and correct question is as under:

What is the probability that the mean clock life would differ from the population mean by greater than 12.5 years?