Question

Assume that​ women's heights are normally distributed with a mean given by mu equals 62.6 in​, and a standard deviation given by sigma equals 1.9 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 63 in. ​(b) If 41 women are randomly​ selected, find the probability that they have a mean height less than 63 in.

Answer 1

Mean = = 62.6

Standard deviation = = 1.9

a)

We have to find P(X < 63)

For finding this probability we have to find z score.

That is we have to find P(Z < 0.21)

P(Z < 0.47) = 0.5834 ( Using z table)

b)

Sample size = n = 41

We have to find P( > 110)

For finding this probability we have to find z score.

That is we have to find P(Z < 1.35)

P(Z < 1.35) = 0.9112

( From z table)