Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.7 years, and standard deviation of 1.7 years.

If 5 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 =  = 6.7

standard deviation =  = 1.7

n = 5

= 6.7

= / n = 1.7/ 5=0.76

Using standard normal table,

P(Z < z) = 6%

= P(Z < z) = 0.06

= P(Z < z ) = 0.06

= P(Z < -1.56 ) = 0.06

z = -1.56

Using z-score formula  

= z * +   

= -1.56*0.76+6.7

= 5.5