Another application for exponential distributions is supply/demand problems. The operator of a pumping station in a small Wyoming town has observed that demand for water on a typical summer afternoon is exponentially distributed with a mean of 75 cfs (cubic feet per second). Let x be a random variable that represents the town's demand for water (in cfs). What is the probability that on a typical summer afternoon, this town will have a water demand x

(a) More than 60 cfs (i.e., 60 < x < ()?

(b) Less than 140 cfs (i.e., 0 < x < 140)?

(c) Between 60 and 100 cfs?

(d) Brain teaser How much water c (in cfs) should the station pump to be 80% sure that the town demand x (in cfs) will not exceed the supply c? First explain why the equation P(0 < x < c) = 0.80 represents the problem as stated. Then solve for c.