Question

The height of women ages 18 to 24 are approxiametly bell shaped with X=64.5 inches and S=2.5 inches. according to the empirical rule, approximately what percentage of the women's height would you expect to fall between:

*explain and show work

a) 62 and 67 inches?

b) 59.5 to 69.5 inches?

c) 57 to 72 inches?

d) if there was a height equal to 77 inches, could you consider such a height and outlier?explain

Answer 1

Mean = = 64.5

Standard deviation = = 2.5

Empirical rule:

1) About 68% of data lies in the 1 standard deviation from the mean.

that is in the interval

2) About 95% of data lies in the 2 standard deviations from the mean.

that is in the interval

3) About 99.7% of data lies in the 3 standard deviations from the mean.

that is in the interval
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a)

= 64.5 - 2.5 = 62

= 64.5 + 2.5 = 67

About 68% of data lies in the 1 standard deviation from the mean.

that is in the interval

68% of the women's height would you expect to fall between 62 and 67 inches.

b)

= 64.5 - 2*2.5 = 59.5

= 64.5 + 2*2.5 = 69.5

About 95% of data lies in the 2 standard deviations from the mean.

that is in the interval

95% of the women's height would you expect to fall between 59.5 and 69.5 inches.

c)

= 64.5 - 3*2.5 = 57

= 64.5 + 3*2.5 = 72

About 99.7% of data lies in the 3 standard deviations from the mean.

that is in the interval

99.7% of the women's height would you expect to fall between 57 and 72 inches.

d)

Any z-score is greater than 3 or less than -3 is considered to be an outlier.

x = 77

Z score is beyond ( -3, 3) so the height equal to 77 inches is an outlier.