You should have your concept of linear functions of random variables.
For a random variable X
For four random variables , which are iid as X,
And
Now what?
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