# random variable?/probability question

• May 26th 2008, 09:01 PM
asdfqwerty
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
• May 27th 2008, 05:56 AM
TKHunny
You should have your concept of linear functions of random variables.

For a random variable X

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

$\displaystyle \sigma_{X} = 10$

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

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

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

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

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

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

Now what?