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.

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 probability of a normally distributed data is given by:



Thus, the probability that a woman completes the 200-meter backstroke in less than 128 seconds is given by:



Therefore, the proportion of competitive female swimmers who will qualify for the nationals is 0.0317 to 4 decimal places.