Assume that womens heights are normally distributed with a m

Assume that women\'s heights are normally distributed with a mean given by mu = 63 1 in, and a standard deviation given by sigma = 2 5 in. If 1 woman is randomly selected, find the probability that her height is loss than 64 in. If 30 women are randomly selected, find the probability that they have a mean height less than 64 In. The probability is approximately (Round to four decimal places as needed.) The probability is approximate (Round to four decimal places as needed )

Solution

a)

P(X < 64) = P(Z < 64 - 63.1 / 2.5)

= P( Z < 0.36)

= 0.6406

b)

P(X < 64) = P(Z < 64 - 63.1/2.5/sqrt(30))

= P( Z < 1.9718)

= 0.9757