# question 8 and 9 for midterm study guide

edited June 30

Did anyone find the standard deviation or mean for questions 8 and 9? Are we just looking at
(1508+1541+232)/3
for the mean and the standard deviation is just
sqrt((1508-1093.66)^2+(1541-1093.66)^2+(232-1093.66)^2)/(n-1)?

• First off, I edited your post to include mathematical typesetting - which is basically just a matter of including percentage symbols around your formulae. One thing that's nice about that is that it forces you to use correct parentheses. For example, you had typed

``````1508+1541+232/3
``````

If you wrap that exactly in percentage symbols, you get

``````1508+1541+232/3
``````

Which typesets like so: 1508+1541+232/3

I suspect, though, that you want all three data points over 3. To get that you should type

``````(1508+1541+232)/3
``````

Having said all that, you're treating this like numerical data when it's actually categorical data. I would treat it like a binomial problem. That is, you pick 50 students and you know that the probability that any one of them is not from WNC is
$$\frac{1541+232}{3281} \approx 0.540384.$$
That gives you a single random variable that could call $X$. I think that the direct answer to your question is that the mean of $X$ is $0.540384$. You find the variance using the formula $p(1-p)$.

If we now let
$$S = X_1 + X_2 + \cdots + X_{50}$$
denote the sum of 50 independent copies of $X$, then the question is "What is the probability that $S$ is greater than 28?" Or $P(S>28) = ?$

You can answer that question with a normal distribution whose mean and variance are the same as the mean and variance of $S$. You find that mean and variance by multiplying the corresponding terms for $X$ by 50.