Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12 years, and standard deviation of 0.5 years. If 5 items are picked at random, 4% of the time their mean life will be less than how many years? Give your answer to one decimal place.

Answer 1

SOLUTION

Given that,

mean = = 12

standard deviation = = 0.5

n = 5

= 12

= / n = 0.5 /5=0.22

Using standard normal table,

P(Z < z) = 4%

= P(Z < z) = 0.04  

= P(Z < -1.75) = 0.04

z = -1.75 Using standard normal table,

Using z-score formula  

= z * +   

= -1.75*0.22+12

= 11.6