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 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 325 seconds.

Answer 1

0.0107 is the probability that a randomly selected boy in secondary school can run the mile in less than 325 seconds.

Explanation:

We are given the following information in the question:

Mean, μ = 440 seconds

Standard Deviation, σ = 50 seconds

We are given that the distribution of time is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(run the mile in less than 325 seconds)

P(x < 325)

`P( x < 325) = P( z < \displaystyle(325 - 440)/(50)) = P(z < -2.3)`

Calculation the value from standard normal z table, we have,

`P(x < 325) = 0.0107 = 1.07\%`

0.0107 is the probability that a randomly selected boy in secondary school can run the mile in less than 325 seconds.