Question:

Suppose the heights (in inches) of men ages 20-29) in the United States are normally distributed with a

mean of 69.3 inches and a standard deviation of 2.92 inches.

Estimate the percentage of 20-29-year old men that meet the following conditions using the Empirical

Rule.

See the explanation below:

16% of the men (ages 20-29) are taller than 72.22 inches.

Explanation:

The alleged conditions indicated in the comments section are wrong, because for a continuous distribution, like the normal distribution, the probability of an exact value is zero.

A real question, for this same statement is:

Determine the percentage of 20 - 29 year old men taller than 72.22 inches.

The empirical rule states tha, for a normal distribution,

68% of data falls within the one standard deviation from the mean. 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Thus, for the heights of men (ages 20 - 29) in the United States:

68% of men's heights are within 69.3 inches ± 2.92 inches, this is in the range 66.38 inches to 72.22 inches. 95% of men's heights are within 69.3 inches ± 2*2.92 inches, this is in the range 63.46 inches to 75.14 inches 99.7% of men's heights are within 69.3 inches ± 3*2.92, this is in the range 60.54 inches to 78.06 inches,

You may, then, determine how many men are taller than 72.22 inches.

72.22 inches is one standard deviation above the mean. Since the normal distibution is symmetric around the mean, you reason in this way:

100% - 68% = 32% are either below or above one standard deviation from the mean half ot that, i. e. 16% are below the mean and half are above the mean thus, 16% are taller than 72.22 inches.