Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.1 years, and standard deviation of 1.1 years.

If 19 items are picked at random, 10% 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 = = 7.1

standard deviation = = 1.1

n = 19

= 7.1

= / n = 1.1/19=0.2524

Using standard normal table,

P(Z < z) = 10%

= P(Z < z) = 0.10  

= P(Z <-1.28 ) = 0.10

z = -1.28 Using standard normal table,   

Using z-score formula  

= z * +

= -1.28 *0.2524+7.1

= 6.8