Assume that womens heights are normally distributed with a m

Assume that women\'s heights are normally distributed with a mean given by mu = 64.5 in, and a standard deviation given by sigma = 2.7 in. If 1 woman is randomly selected, find the probability that her height is less than 65 in. If 48 women are randomly selected, find the probability that they have a mean height less than 65 in. The probability is approximately . (Round to four decimal places as needed.) The probability is approximately . (Round to four decimal places as needed.)

Solution

(a) P(X<65) = P((X-mean)/s <(65-64.5)/2.7)

=P(Z<0.19) =0.5753 (from standard normal table)

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(b) P(xbar<65) = P((xbar-mean)/(s/vn) <(65-64.5)/(2.7/sqrt(48)))

=P(Z<1.28) =0.8997 (from standard normal table)