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 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 335 seconds to run the mile.

A) 0.5107


B) 0.9893


C) 0.0107


D) 0.4893

Answer 1

The probability that a randomly selected boy in secondary school will

take longer than 335 seconds to run the mile is 0.9893 ⇒ answer B

Explanation:

- 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 450 seconds and a

standard deviation of 50 seconds

∴ μ = 450 seconds

∴ σ = 50 seconds

- We need to find the probability that a randomly selected boy in

secondary school will take longer than 335 seconds to run the mile

- We must to find z-score for x > 335 seconds

∵ z = (x - μ)/σ

∵ x = 335 seconds , μ = 450 seconds , σ = 50 seconds

- substitute the values in the rule above

∴ z =
`(335-450)/(50)` = -2.3

- Use the normal distribution table of z to find the corresponding area

of z-score

∵ P(-2.3) = 0.01072

- We need to find the area to the right of the z-score

∴ P( x > 335) = 1 - 0.01072 = 0.9893

* The probability that a randomly selected boy in secondary school

will take longer than 335 seconds to run the mile is 0.9893