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In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.
<u><em>Explanation</em></u>
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...
That means, <em>(in whole number)</em>
So, in order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.
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