Question

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 possess a normal distribution with a mean of 440 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 302 seconds.

Answer 1

The probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds is 0.0107

Explanation:

Consider the provided information.

It is given that mean is 440 seconds and standard deviation is 60 seconds.

z factor for less than 302 seconds would be:
`z=(x-\mu)/(\sigma)`

z = (302 - 440) / 60 = -2.3

The probability of getting a z factor of less than -2.3 = 0.0107 approximately.

looking up in the z-table for a z factor of -2.3.

The probability of a student running the mile in less then 302 seconds would be 0.0107.

Hence, the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds is 0.0107