Question

Assume that women's heights are normally distributed with a mean given by mu equals 63.6 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 39 women are randomly selected, find the probability that they have a mean height less than 64 in. (a) The probability is approximately nothing. (Round to four decimal places as needed.) (b) The probability is approximately nothing. (Round to four decimal places as needed.)

Answer #1

Population mean, = 63.6

Standard deviation, = 2.4

(a) Probability that a randomly selected woman has height less than 64 in. = P(X < 64)

Corresponding z value = (64 - 63.6)/2.4 = 0.167

Thus required probability = P(z < 0.167) =
**0.5662**

(b) For n = 39 randomly selected woman, the standard error of mean height

= /√n = 2.4/√39 = 0.3843

The required probability = P( < 64)

Corresponding z value = (64 - 63.6)/0.3843 = 1.042

The probability is P(Z < 1.042) = **0.8512**

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