Question

Solve the problem. Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years. Write your answer as a decimal rounded to 4 places.

Answer 1

$\mu$ = 9.3

$\sigma$ = 1.1

n = 70

SE = $\sigma$ /$\sqrt{n}$

= 1.1/$\sqrt{70}$ = 0.1315

To find P($\bar{x}$< 9.1):

Z = ($\bar{x}$ - $\mu$ )/SE

=(9.1 - 9.3)/0.1315 = - 1.5212

Table of Area Under Standard Normal Curve gives area = 0.4357

So

P($\bar{x}$<9.1) = 0.5 - 0.4357 = 0.0643

So,

Answer is:

0.0643