A random sample of size 975 is drawn from a large population. The population standard deviation is 18.

Question

A random sample of size 975 is drawn from a large population. The population standard deviation is 18. The sample mean is 69.2. Find a 99% confidence interval for the population mean, 𝜇.

(a) 66.7 < 𝜇 < 71.7

(b) 67.7 < 𝜇 < 70.1

(c) 67.7 < 𝜇 < 70.7

Answer 1

There are two ways to solve this problem with the formula and the calculator.

The formula is the following:

X-bar ± z* σ/√n

For this for problem this is how you would set up the formula:

69.2± 2.576* 18/ √975

Confidence interval is :

( 66.7< µ < 70.7)

If you are using the calculator you will be using the function ZInterval

ZInterval

σ=18

x-bar=69.2

n=975

C-level=0.99

Confidence interval is:

( 66.7< µ < 70.7)