Heights of a sample of male college students have a mean of 71 inches and a stan

Question

Heights of a sample of male college students have a mean of 71 inches and a standard deviation of 3 inches. How many standard deviations from the mean is a male student athlete who is 84 inches tall?

This athlete has a z-score of 13.00, so his height is 13.00 standard deviations above the mean.

This athlete has a z-score of 3.33, so his height is 3.33 standard deviations above the mean.

This athlete has a z-score of 4.33, so his height is 4.33 standard deviations above the mean.

This athlete has a z-score of negative 4.33, so his height is 4.33 standard deviations below the mean.

Explanation / Answer

Solution

Answer: This athlete has a z-score of 4.33, so his height is 4.33 standard deviations above the mean.

Because,

Z score = (score – mean)/SD = (84 - 71)/3 = 4.33 => 84 is 4.33 times standard deviation above the mean.

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