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 16 years with a standard deviation of 5 years. If the claim is true, in a sample of 32 wall clocks, what is the probability that the mean clock life would be greater than 15.6 years? Round your answer to four decimal places.

Answer 1

Answer:

0.6745 is the probability that the mean clock life would be greater than 15.6 years.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 16 years

Standard Deviation, σ = 15 years

Sample size, n = 32

Standard error due to sampling =

$=\dfrac{\sigma}{\sqrt{32}} = \dfrac{5}{\sqrt{32}} = 0.8838$

We assume that the distribution of clock life is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(mean clock life would be greater than 15.6 years)

P(x > 15.6)

$P( x > 15.6) = P( z > \displaystyle\frac{15.6 - 16}{0.8838}) = P(z > -0.4525)$

$= 1 - P(z \leq -0.4525)$

Calculation the value from standard normal z table, we have,  

$P(x > 15.6) = 1 - 0.3255 = 0.6745 = 67.45\%$

0.6745 is the probability that the mean clock life would be greater than 15.6 years.