## A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 17 years with

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 17 years with a standard deviation of 4 years. If the claim is true, in a sample of 48 wall clocks, what is the probability that the mean clock life would be greater than 18 years

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2 months 2021-10-08T22:47:50+00:00 1 Answer 0 views 0

Probability that the mean clock life would be greater than 18 years is 0.04182 .

Step-by-step explanation:

We are given that the designer claims they have a mean life of 17 years with a standard deviation of 4 years.

Let X bar = mean clock life

The z score probability distribution is given by;

Z = ~ N(0,1)

where,   = population mean life = 17 years

= standard deviation = 4 years

n = sample of wall clocks = 48

So, the probability that the mean clock life would be greater than 18 years is given by, P(X bar > 18 years);

P(X bar > 18) = P( < ) = P(Z > 1.73) = 1 – P(Z <= 1.73)

= 1 – 0.95818 = 0.04182

Therefore, the probability that the mean clock life would be greater than 18 years is 0.04182 .