Question

A physical fitness association is including the mile run in its secondary-school fitness test. The time for thisevent for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds.

Answer 1

Answer:  0.0107

Step-by-step explanation:

Given : The time for the event for boys in secondary school is known to possess a normal distribution with

$\mu=460\text{ seconds}\\\\\sigma=20\text{ seconds}$

Let x be the random variable that represents the time for mile run in its secondary-school fitness test.

z-score : $\dfrac{x-\mu}{\sigma}$

$z=\dfrac{322-460}{60}=-2.3$

Now, the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds is given by :-

$P(x<322)=P(z<-2.3)=0.0107241\approx0.0107$

Hence, the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds = 0.0107