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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 distribution.

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:

a) 2.5% of adult males are under 64 inches tall.

b) 81.5% of adult males are between 64 and 73 inches tall.

What does the Empirical Rule state?

It states that, for a normally distributed random variable, 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.

For item a, we have that 64 is two standard deviations below the mean, hence, considering the symmetry of the normal distribution:

2.5% of adult males are under 64 inches tall.

As shown by the first graph at the end of the answer.

For item b, we have that 64 is two standard deviations below the mean, while 73 is one above, hence, considering the symmetry of the normal distribution:

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

As shown by the two blue sections, plus the left brown section, in the second graph.

More can be learned about the Empirical Rule at https://brainly.com/question/20875827

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