ACME manufacturing company has developed a fuel-efficient machine that

combines pressure washing with steam cleaning. It is advertised as

delivering 5 gallons of cleaner per minute. HOWEVER, a machine

delivers an amount at random anywhere between 2 and 6 gpm.

Assume that Y, the amount of cleaner dispensed per minute,

is a uniform random variable with probability density function

[p.d.f.], f(y), given below.

{ 1/4 2 <= y <= 6

f(y) = {

{ 0 otherwise

a.) Find the probability that Y, the amount of cleaner dispensed per minute, is greater than 5 gallons per minute.

b.) Find the expected value of Y, E(Y).

Find the variance value of Y, VAR(Y).

c.) Suppose a random sample of 9 pressure washing machines are to be tested and the sample mean, YBAR, calculated. Find the probability that the sample mean, YBAR, is greater than 5 gallons per minute.

What did you assume in order to calculate this probability?

d.) What happens to the probability in part c. (that the sample mean, YBAR, is greater than 5 gallons per minute) as the size n of the random sample increases? Does it stay same?

Please help. I am completely lost with where to start/how to start. Any help would be greatly appreciated!