Question

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 replacement time that separates the top 3% from the bottom 97% . Round your answer to 3 decimal places.

Answer 1

Solution:-

Given that,

mean = = 9.3

standard deviation = = 1.1

Using standard normal table,

P(Z > z) = 3%

= 1 - P(Z < z) = 0.03

= P(Z < z) = 1 - 0.03

= P(Z < z ) = 0.97

= P(Z <1.88 ) = 0.97  

z =1.88 ( using z table )

Using z-score formula,

x = z * +

x = 1.88 * 1.1+9.3

x = 11.368