# Math Help - Physical Fitness Probability

1. ## Physical Fitness Probability

I need help please....

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to process a normal distribution with a mean of 440sec and a standard deviation of 50sec. The fitness association wants to recorgnize the fastest 10% of the boys with certificates of recorgnition. What time would the boys need to beat in order to earn a certificate of recorgnition from the fitness association?

2. $\mu = 440 \; \mbox{ and } s = 50$

You need that $P(z>x) = 0.1$ , where z is your random variable. Now we need to find x.

Looking at normal distribution table we find the 10% quantile being approximatively 1.28 standard deviations.

So we get, $\mu - 1.28 \cdot s = 440 - 1.28 \cdot 50 = 376 \mbox{ seconds}$