A physical fitness association is including the mile run in

A physical fitness association is including the mile run in the secondary-school fitness test. The time for this for this event for boys in secondary school is know to possess a normal distribution with a mean of 470 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

Solution

P(X<x)=0.1

--> P((X-mean)/s <(x-470)/40)=0.1

--> P(Z<(x-470)/40) =0.1

--> (x-470)/40 = -1.28 (from standard normal table)

So x= 470 -1.28*40 =418.8