A.Suppose X is the weight of boxes of butter (in kilograms) shipped between two countries. It is known that E(X) =25

and var(X)=4.

1.What is the mean and variance of Y = 0.5X - 12.5. Show your work. (3 points)

2. What is the probability that a box drawn randomly from a shipment would have a weight (a) greater than 26.5 kg.

(b) less than 24 kg? (c) between 22kg and 25 kg (3 points)

B. Consider the following probability distribution:

x:01234

f(x):b2b3b4b5b

Determine the value of the constant b, and then find the mean and variance of X. (4 points)

Parts A and B unrelated