Answer to Question #286216 in Statistics and Probability for gau

Question

The average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these machines follow approximately a normal distribution, find the value of the sample mean to the right of which 15% of the means computed from random samples of size 9 would fall.

Answer 1

$P(Z>z)=0.15.$

$P(Z<z)=0.85.$

$z=1.04.$

$\frac{\bar x-7}{\frac{1}{\sqrt{9}}}=1.04.$

$\bar x=7+\frac{1.04}{3}=7.35.$