A small company that makes fiberglass surfboards. The molding process is very tricky, and results in defects exactly 25% of the time, and this probability is independent of how many other defects there have been that week. You attempt to mold exactly 10 surfboards every week. Let the random variable X indicate the number of non-defective surfboards you produce in any given week.

a.) What are the possible values for X?

b.) Give the entire distribution (probability mass function) for X.

c.) What is the average number of non-defective surfboards you make per week?

d.) What is the variance in the number of surfboards you make per week?

e.) State completely the cumulative distribution function for X.

f.) What is the probability that you produce 7 or more non-defective surfboards in a given week?

g.) If the profit you make is $100 per non-defective surfboard produced in the week minus $450 in fixed costs, what is the average profit you make per week, and what is the variance?