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Assume that women\'s heights are normally distributed with a mean given by mu =6

ID: 3245638 • Letter: A

Question

Assume that women's heights are normally distributed with a mean given by mu =624 in, and a standard deviation given by sigma = 1.8 in. (a) It 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 33 women are randomly selected, find the probability that they have a mean height lee than 63 in. (a) The probability is approximately __. (Round to four decimal places as needed.) (b) The probability is approximately __. (Round to four decimal places as needed.)

Explanation / Answer

a)

P(X < 63) = P(Z < 63 - 62.4/1.8)

= P(Z < 0.3333)

= 0.6306

b)

P(X < 63) = P(Z < 63 - 62.4/1.8/sqrt(33))

= P(Z < 1.9149)

= 0.9722