Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.5 years, and standard deviation of 1.2 years.

If 9 items are picked at random, 6% 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 = = 7.5

standard deviation = = 1.2

n = 9

= 7.5

= / n = 1.2/9=0.4

Using standard normal table,

P(Z < z) = 6%

= P(Z < z) = 0.06  

= P(Z <-1.56)=0.06

Using z-score formula  

= z * +   

= -1.56*0.4+7.5

= 6.9