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 16 years with a variance of 16. If the claim is true, in a sample of 48 wall clocks, what is the probability that the mean clock life would differ from the population mean by greater than 0.7 years? Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 16

standard deviation = = 4

= / n = 4 / 48 = 0.5774

= 1 - P[(-0.7) / 0.5774< ( - ) / < (0.7) / 0.5774)]

= 1 - P(-1.21 < Z < 1.21)

= 1 - P(Z < 1.21) - P(Z < -1.21)

= 1 - P(0.8869 - 0.1131)

= 1 - 0.7738

= 0.2262

Probability = 0.2262

orchestra answered 2 years ago
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