Question

In: Statistics and Probability

A production manager at a wall clock company wants to test their new wall clocks. The...

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 1414 years with a variance of 1616.

If the claim is true, in a sample of 4040 wall clocks, what is the probability that the mean clock life would differ from the population mean by less than 0.40.4 years? Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 14

standard deviation = = 4

= / n = 4 / 40 = 0.6325

= P[(-0.4) / 0.6325< ( - ) / < (0.4) / 0.6325)]

= P(-0.63 < Z < 0.63)

= P(Z < 0.63) - P(Z < -0.63)

= 0.7357 - 0.2643

= 0.4714

Probability = 0.4714

orchestra answered 2 years ago
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