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.
Now 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.

The swimmer must complete the 200-meter backstroke in no more than 130 seconds.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Fastest 6%

At most in the 6th percentile, that is, at most a value of X when Z has a pvalue of 0.07. So we have to find X when Z = -1.555.

The swimmer must complete the 200-meter backstroke in no more than 130 seconds.

its 69.420

step-by-step explanation: