Question

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. suppose the fastest 6% of female swimmers in the nation are offered college scholarships. in order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than how many seconds? give your answer in whole numbers

Answer 1

In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.

Explanation

Given that the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds

The fastest 6% of female swimmers in the nation are offered college scholarships. So, the probability will be 0.06

According to the normal distribution table, the z-score for probability of 0.06 is   0.5239

Now using z-score formula z= (x- μ)/σ , we will get...

$0.5239= \frac{x-141}{7}\\ \\ x-141= 3.6673\\ \\ x= 3.6673+141 \\ \\ x= 144.6673$

That means, $x < 144$ (in whole number)

So, in order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.