Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10 years, and standard deviation of 1.8 years.

If 20 items are picked at random, 2% 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 = = 10

standard deviation = = 1.8

n = 2

= 10

= / n =1.8 /2=1.27

Using standard normal table,

P(Z < z) = 2%

= P(Z < z) = 0.02

= P(Z <-2.05 ) = 0.02

z = -2.05    Using standard normal table,

Using z-score formula  

= z * +   

= -2.05*1.27+10

= 7.4