Answer:
See the explanation below:
- <u>16% of the men (ages 20-29) are taller than 72.22 inches.</u>
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:
- <em>Determine the percentage of 20 - 29 year old men taller than 72.22 inches.</em>
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 <em>how many men are taller than 72.22 inches.</em>
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.
