Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. How fast does a man have to run to be in the top 1% of runners (quickest runner)?

To be in the top 1% of runners, a man has to run the 400m in at most 55.8 seconds.

Step-by-step explanation:

Problems of normally distributed samples can be 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:

How fast does a man have to run to be in the top 1% of runners (quickest runner)?

Quickest runner means that he ran in the least time, that is, his time is in the 1st percentile. So it is values of X and lower, in which X is found when Z has a pvalue of 0.01. So X when Z = -2.325.

To be in the top 1% of runners, a man has to run the 400m in at most 55.8 seconds.

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step-by-step explanation:

step-by-step explanation:

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