Question

Assume that women’s heights are normally distributed with a mean given by 63.3 in, and a standard deviation given by SD = 2.9 in. (a) if 1 woman is randomly selected, find the probability that her height is between 62.6 in and 63.6 in. (b) If 8 women are randomly selected, find the probability that they have a mean height between 62.6 and 63.6 in.

Answer 1

Part a)

P ( 62.6 < X < 63.6 )
Standardizing the value

Z = ( 62.6 - 63.3 ) / 2.9
Z = -2
Z = ( 63.6 - 63.3 ) / 2.9
Z = -1
P ( -2 < Z < -1 )
P ( 62.6 < X < 63.6 ) = P ( Z < -1 ) - P ( Z < -2 )
P ( 62.6 < X < 63.6 ) = 0.1587 - 0.0228
P ( 62.6 < X < 63.6 ) = 0.1359

Part b)

P ( 62.6 < X < 63.6 )
Standardizing the value


Z = -0.68

Z = 0.29
P ( -0.68 < Z < 0.29 )
P ( 62.6 < X < 63.6 ) = P ( Z < 0.29 ) - P ( Z < -0.68 )
P ( 62.6 < X < 63.6 ) = 0.6151 - 0.2474
P ( 62.6 < X < 63.6 ) = 0.3677