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Assume that women’s heights are normally distributed with a mean given by u=63.9

ID: 3324678 • Letter: A

Question

Assume that women’s heights are normally distributed with a mean given by u=63.9 in., and a standard deviation given by o=3.1 in. Complete parts a and b.
A. if 1 woman is randomly selected, find the probability that her height is between 63.2 in and 64.2 in.
B. If 11 women are randomly selected, find the probability that they have a mean height between 63.2 in and 64.2 in. Assume that women’s heights are normally distributed with a mean given by u=63.9 in., and a standard deviation given by o=3.1 in. Complete parts a and b.
A. if 1 woman is randomly selected, find the probability that her height is between 63.2 in and 64.2 in.
B. If 11 women are randomly selected, find the probability that they have a mean height between 63.2 in and 64.2 in.
A. if 1 woman is randomly selected, find the probability that her height is between 63.2 in and 64.2 in.
B. If 11 women are randomly selected, find the probability that they have a mean height between 63.2 in and 64.2 in.

Explanation / Answer

A) P(63.2 < X < 64.2) = P((63.2-63.9)/3.1 < Z < (64.2-63.9)/3.1)

= P(-0.23 < Z < 0.1)

= P(Z < 0.1) - P(Z < - 0.23)

= 0.5398 - 0.4090

= 0.1308

B) P(63.2 < X bar <64.2) = P((63.2-63.9)/(3.1/sqrt(11)) < Z < (64.2-63.9)/(3.1/sqrt(11)))

= P(-0.75 < Z < 0.32)

= P(Z < 0.32) - P(Z < - 0.75)

= 0.6255 - 0.2266

= 0.3989