Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.4 years, and standard deviation of 0.6 years. If 13 items are picked at random, 8% of the time their mean life will be less than how many years? Give your answer to one decimal place.

Answer 1

Given that,

mean = = 7.4

standard deviation = = 0.6

n = 13

= 7.4

= / n = 0.6 /13=0.1664

Using standard normal table,

P(Z < z) = 8%

= P(Z < z) = 0.08  

= P(Z <-1.41 ) = 0.08

z = -1.41 Using standard normal table,

Using z-score formula  

= z * +   

=-1.41 *0.1664+7.4

= 7.2