Assuming that the heights of college women are normally distributed with mean 62

Question

Assuming that the heights of college women are normally distributed with mean 62 inches and standard deviation 2.7 inches, answer the following questions. (Hint: Use the figure below with mean and standard deviation.) Area Under a Normal Curve 2.35%, 13.5% | 34% | 34% | 13.5% 2.35% 68% 95% 99.7% (a) What percentage of women are taller than 62 inches? (b) What percentage of women are shorter than 62 inches? (c) What percentage of women are between 59.3 inches and 64.7 inches? (d) What percentage of women are between 56.6 and 67.4 inches?

Explanation / Answer

Mean = 62

SD = 2.7

A) P(X > 62) = 50%

B) P(X < 62) = 50%

C) 59.3 = 62 - 2.7 = mean - SD

64.7 = mean + SD

So, P(59.3 < X < 64.7) = 68%

D) 56.6 = 62 - 2*2.7 = mean - 2*SD

67.4 = mean + 2*SD

P(56.6 < X < 67.4) = 95%

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