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. Using the Empirical Rule, 95% of adult males should fall into what height range?

About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.

Using the empirical rule :

95% will fall between + or - 2 standard deviation of the mean.

Lower limit = - 2(3) = - 6

Upper limit = 2(3) = 6

(-6+mean) and (+6+ mean)

(-6 + 70) and (6+70)

64 and 76

nishantwork777 nishantwork777 · Answer 2 · 2021-12-09T12:43:27+01:00

The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

According to the given data

The mean height for adult males in the U.S. is about 70 inches

The standard deviation of heights is about 3 inches.

Considering the data to be normally distributed

According to the empirical rule for normal distribution we can write that

95.45% of the data lies with in the range of

[tex]\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation[/tex]

We have to to determine that using the Empirical Rule 95% of adult males should fall into what height range

According to the given data

[tex]\rm \mu = 70\\\rm \sigma = 3 \\[/tex]

[tex]\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64[/tex]

[tex]\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76[/tex]

So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

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