Question

A company makes car shocks. The distance traveled before the shocks fail is normally distributed with a mean of 75,000 miles and a standard deviation of 10,000 miles. At about what number of miles is there a 80% chance that the shock will have failed?

Answer 1

Given that,

mean =  = 75000

standard deviation =  = 10000

Using standard normal table,

P(Z < z) = 80%

=(Z < z) = 0.80  

= P(Z < z ) = 0.80  

z = 0.84   

Using z-score formula  

x = z +

x = 0.84 *10000+75000

x = 83400