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Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about 3 inches. Assume men’s heights follow a normal curve.

a) What percentage of adult males are under 64 inches tall? Use the 68-95-99.7 rule and draw a picture that illustrates your rationale.

b) What percentage of adult males are between 64 and 73 inches tall? Use the 68-95-99.7 rule and draw a picture that illustrates your rationale.

Answer :

Using the Empirical Rule, it is found that the percentages are given as follows:

a) 2.5%.

b) 81.5%.

What does the Empirical Rule state?

It states that, for a variable that has a normal distribution, approximately:

  • 68% of the values in the distribution are within 1 standard deviation of the mean.
  • 95% of the values in the distribution are within 2 standard deviations of the mean.
  • 99.7% of the values in the distribution are within 3 standard deviations of the mean.

The mean and the standard deviation of the heights are given as follows:

  • Mean of 70 inches.
  • Standard deviation of 3 inches.

Hence, in item a, we have that 64 is two standard deviations below the mean, and considering the symmetry of the normal distribution, 2.5% of the heights are below that.

For item b, the range is between two below and one above, hence the percentage is:

P = 0.5 x 95 + 0.5 x 68 = 81.5%.

The graph given at the end of the answer shows the distribution of heights according to the 68-95-99.7 rule.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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