Assume that women's heights are normally distributed with a mean given by mu equals 63.4 in , and a standard deviation given by sigma equals 2.4 in. (a) if 1 woman is randomly selected, find the probability that her height is less than 64 in. (b) if 44 women are randomly selected, find the probability that they have a mean height less than 64 in.

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Mathematics

Gardner

5 May, 03:59

Assume that women's heights are normally distributed with a mean given by mu equals 63.4 in , and a standard deviation given by sigma equals 2.4 in. (a) if 1 woman is randomly selected, find the probability that her height is less than 64 in. (b) if 44 women are randomly selected, find the probability that they have a mean height less than 64 in.

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Garner · Answer 1

(a) Using a suitable probability calculator, the probability is 0.5987.

(b) The calculation is done the same way, but the population sigma is divided by the square root of the sample size. The probability is 0.9514.