Question

The mean height of women in a country (ages 20-29) is 63.6 inches. A random sample of 70 women in this age group are selected. What is the probability that the mean height for the sample is greater than 64 inches?Assuming sigma= 2.53 inches

Answer 1

We have a mean of 63.6 inches and a standard deviation of 2.53 inches. We want to find the probability for our random sample to have a greater mean than 64 inches. We can do that by finding the probability of getting women higher than 64 inches in the original group. To do that, we're going to use a z-table.

First, let's convert 64 inches to a z-score:

`\begin{gathered} z(64)=\frac{64-\mu}{\sigma/\sqrt[]{n}}=\frac{64-63.6}{2.53/\sqrt[]{70}}=\frac{0.4\sqrt[]{70}}{2.53}=1.32278265065\ldots \\ z(64)\approx1.32 \end{gathered}`

Using a right z-table, we have

This z-table gives us the area between the middle of the bell curve and our desired value.

This means, the probability of getting a sample higher than our value, will be 0.5 minus the probability given by the z-table.

`0.5-0.4066=0.0934`

Then, we have our result.

`P(\bar{x}>64)=0.0934`