Let SALES denote the monthly sales at a bookstore. Assume SALES are normally distributed with a mean of \(\$ 50,000\) and a standard deviation of \(\$ 6000\).

a. Compute the probability that the firm has a month with SALES greater than \(\$ 60,000\). Show a sketch.

b. Compute the probability that the firm has a month with SALES between \(\$ 40,000\) and \(\$ 55,000\). Show a sketch.

c. Find the value of SALES that represents the 97th percentile of the distribution. That is, find the value \(S A L E S_{0.97}\) such that \(P\left(S A L E S>S A L E S_{0.97}\right)=0.03\).

d. The bookstore knows their PROFITS are \(30 \%\) of SALES minus fixed costs of \(\$ 12,000\). Find the probability of having a month in which PROFITS were zero or negative. Show a sketch.