# Homework 7 #1 and #2

- Suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. In a group of ten such patients, the number who recover would have mean and variance respectively given by (to one decimal place):

I found the mean but am having trouble finding the variance. For this one I was thinking (.8*.68)^2, but that is incorrect. What am I missing here?

2.The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1220 who were over the age of 25, and 1051 of them were high school graduates.

(a) Find the mean and standard deviation for the number of high school graduates in groups of 1220 Americans over the age of

26.

I found the mean but can't find the standard deviation. I tried (.82*.68)*1220 then took the square root of that, which was 26.08. What am I doing wrong?

I know standard deviation and variance are related and know that I must be missing something.

Thanks!

## Comments

Well, I'm not sure where you got your $(0.8\times0.68)^2$ from. In this problem, we have $p=0.8$ so the formula for variance yields:

$$

\sigma^2 = p(1-p) = 0.8\times0.2 = 0.16.

$$

Then, you take the square root to get the standard deviation.

I think that the next one is similar but, now, $p=0.82$.