0
$\begingroup$

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

What is the formula for going about this problem? I am searching through my textbook, but cant seem to find out how to solve this. The random sample of four is the part that is throwing me off.

$\endgroup$
  • $\begingroup$ If x has a normal distribution, what can we say about the distribution of $\bar{x}$? $\endgroup$ – Brad S. Mar 26 '14 at 0:28
1
$\begingroup$

Hint:

Say that your four sampled heights are $X_1,X_2,X_3,X_4$. These are independent random variables that are normally distributed with mean $64$ and standard deviation $2$.

The question is then asking you for $$ P\left(\frac{X_1+X_2+X_3+X_4}{4}\geq66\right). $$

$\endgroup$
  • $\begingroup$ I tried 66 divided by four using the logic above, but it is asking for a decimal answer to four places. I plugged it into a normal distribution function on excel but that is not working either. $\endgroup$ – Jake Nagel Mar 26 '14 at 1:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.