Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean equals 136 days and standard deviation equals 12 days.

What is the probability a random sample of size 19 will have a mean gestation period within 8 days of the​ mean

Answer 1

Population mean, = 136 days

Population standard deviation, = 12 days

Sample size, n = 19

Sample mean, = = 136 days

Sample standard deviation, =

=

= 2.753

P( < A) = P(Z < (A - )/)

P(a random sample of size 19 will have mean gestation period within 8 days of the​ mean) = P(128 < < 144)

= P( < 144) - P( < 128)

= P(Z < (144 - 136)/2.753) - P(Z < (128 - 136)/2.753)

= P(Z < 8/2.753) - P(Z < -8/2.753)

= P(Z < 2.91) - P(Z < -2.91)

= 0.9982 - 0.0018

= 0.9964