Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean (μ) = 227 days and standard deviation (σ) = 11 days

Complete parts​ (a) through​ (f) below.

​(f) What is the probability a random sample of size 20 will have a mean gestation period within 8 days of the​ mean?

The probability that a random sample of size 20 will have a mean gestation period within 8 days of the mean is ______________________ (do not round)

Answer 1

Solution:

Given, the Normal distribution with,

   = 227

= 11

A sample of size n = 20 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 227

SD =      = 11/​20 = 2.45967477525

P(Sample mean is within 8 of the population mean)

= P[227 - 8 < < 227 + 8]

= P(219 < < 235)

= P( < 235) - P( < 219)

= P[( - )/ < (235 - 227)/2.45967477525] - P[( - )/ < (219 - 227)/2.45967477525]

= P[Z < 3.25246251273] - P[Z < -3.25246251273]

=  0.999427951568 - 0.000572048432 (use z table)

= 0.998855903137

Answer : 0.998855903137