Question

A physical fitness association is including the mile run units 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 475 seconds and a standard deviation of 65 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 354 seconds to run the mile.

Answer 1

Here the variable(x) is the time taken to run the mile by the boys in secondary school.

As per question we have µ=475 seconds

                                  and σ= 65 seconds

Here, we have to find the probability that a randomly selected boy in secondary school will take longer than 354 seconds to run the mile which means we have to find p(x≥354)

To find out probability from normal distribution we need to convert x values into z values

The z values can be obtained as

For x=354,

That means we have to find p(z≥-1.8615)

From symmetry of normal curve, we know that p(z≥-1.8615)= p(z≤1.8615)

From standard normal table we can find the probability of z≤1.8615

p(z≤1.8615) = 0.9686659 ≈ 0.97

The probability that a randomly selected boy in secondary school will take longer than 354 seconds to run the mile is 0.97