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?

To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

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

The lower the time, the faster they are. So the man has to be at most in the 1st percentile, which is X when Z has a pvalue of 0.01. So he has to run in at most X seconds, and X is found when Z = -2.327. Then

To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

depends what are you allowed to do ?