Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5 years, and standard deviation of 0.7 years.

If 20 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

Solution :

Given that,  

mean = = 5

standard deviation = = 0.7

Sample size = n = 20

= / n = 0.7 / 20 = 0.1565

Using standard normal table ,

P(Z < z) = 6%

P(Z < z) = 0.06

P(Z < -1.56) = 0.06

z = -1.56

Using z-score formula,

x = z * +

x = -1.56 * 0.1565 + 5 = 4.8

6% of the time their mean life will be less than is 4.8 years