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.

Question

Mathematics

Evie Montes

28 July, 20:27

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.

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Brittany Santos · Answer 1

Answer: The proportion that will qualify is 0.0314 or 3.14%.

First, we need to find the z-score of a time of 128 seconds. To do this, we find the difference of the mean and score and divide by the standard deviation.

(128 - 141) / 7 = - 1.86

Now, use a standard normal distribution table to determine the percent below a z-score of - 1.86. That value is 0.0314 or 3.14%.