Question

# Assume that​ women's heights are normally distributed with a mean given by mu equals 63.6 in​,...

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.)

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.