P.8 The Shoulder and Knee Clinic knows that their expected monthly revenue from patients depends on their level of advertising. They hire an econometric consultant who reports that their expected monthly revenue, measured in $1000 units, is given by the following equation E(REVENUE|ADVERT) = 100 + 20 ADVERT, where ADVERT is advertising expenditure in $1000 units. The econometric consultant also claims that REVENUE is normally distributed with variance var(REVENUE|ADVERT) = 900. a. Draw a sketch of the relationship between expected REVENUE and ADVERT as ADVERT varies from 0 to 5. b. Compute the probability that REVENUE is greater than 110 if ADVERT = 2. Draw a sketch to illustrate your calculation. c. Compute the probability that REVENUE is greater than 110 if ADVERT = 3. d. Find the 2.5 and 97.5 percentiles of the distribution of REVENUE when ADVERT = 2. What is the probability that REVENUE will fall in this range if ADVERT = 2? e. Compute the level of ADVERT required to ensure that the probability of REVENUE being larger than 110 is 0.95