Question

question 1 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 that to qualify for the nationals, a woman must complete the 200 - meter backstroke in less than 128 seconds. what proportion of competitive female swimmers will qualify for the nationals? give your answer to four (4) decimal places. click here to download the normal table. .0316

Explanation:

Step1: Calculate z - score

$z=\frac{x-\mu}{\sigma}=\frac{128 - 141}{7}=\frac{-13}{7}\approx - 1.86$

Step2: Find proportion from z - table

Looking up - 1.86 in z - table gives 0.0314.

Answer:

0.0314