Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X.

X 0 1 2 3 4 or more
Probability 0.58 0.23 0.11 0.05 0.03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.

(a) Construct the probability distribution of the random variable Y.

(b) Determine the mean and standard deviation of Y. Show your work.

Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each, but are discounted by $1.50 for each defect found.

(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company G?