1. ## random variable?/probability question

I normally can figure out these straightforward statistics problems, but this one has got me stumped! Thanks in advance to anybody who offers insight.

A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation 10 pounds. If the weights of individuals passengers are independent, what is the probability that a group of four adult males passengers will exceed the acceptable weight limit of 800 pounds?

(A) 0.023
(B) 0.046
(C) 0.159
(D) 0.317
(E) 0.977

2. You should have your concept of linear functions of random variables.

For a random variable X

$\mu_{X} = 190 = E[X]$

$\sigma_{X} = 10$

$\sigma_{X}^{2} = 100 = Var(X)$

For four random variables $X_{i}$, which are iid as X, $i \epsilon \{1, 2, 3, 4\}$

And $Y = X_{1}+X_{2}+X_{3}+X_{4}$

$E[Y] = 4*E[X] = 4*190 = 760$

$Var(Y) = 4*Var(X) = 4*100 = 400$

$\sigma_{Y} = \sqrt{400} = 20$

Now what?