Question

Assume that women's heights are normally distributed with a mean given by

mu equals 63.3 inμ=63.3 in ,

and a standard deviation given by

sigma equals 2.8 inσ=2.8 in.

(a) If 1 woman is randomly selected, find the probability that her height is less than

6464

in.

(b) If

3737

women are randomly selected, find the probability that they have a mean height less than

6464

in.

Answer 1

Solution :

Given that ,

mean = = 63.3

standard deviation = = 2.8

a)

P(x < 64) = P((x - ) / < (64 - 63.3) / 2.8)

= P(z < 0.25)

= 0.5987

Probability = 0.5987

b)

n = 37

= = 63.3 and

= / n = 2.8 / 37 = 0.4603

P( < 64) = P(( - ) / < (64 - 63.3) / 0.4603)

= P(z < 1.52)

=0.9357

Probability = 0.9357