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