The heights of 10000 women students at Eastern College are known to be normally distributed, with a mean of 67 inches and a standard deviation of 3 inches. How many women would you expect to be shorter than 5 ft 1 inch?

Question

Mathematics

Kamila Sampson

14 June, 19:39

The heights of 10000 women students at Eastern College are known to be normally distributed, with a mean of 67 inches and a standard deviation of 3 inches. How many women would you expect to be shorter than 5 ft 1 inch?

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Reese · Answer 1

First, convert 5ft 1inch in inches, you will get 61inches, so the probability that you need to find is P (x≤5)

Find z score: Z = (61-67) / 3 = - 2, with this find the probability from the z table and you get 0.0228 = 2.28%, for the answer multiply 10000 by the probability 0.0228*10000 = 228 women expected to be shorter that 5ft 1inch (61inches)