3. Let F be an RV that represents the operating temperature in Fahrenheit of one instance of a manufacturing process, and let F ∼ N(90, 5 2 ). Let C be an RV that represents the same process, but measured in Celsius. Fahrenheit can be converted to Celsius using C = 5 9 (F − 32). (I recommend doing these with a calculator and N(0, 1) table as practice for the exam. Then check your answers with R if you wish.) (a) Find the probability that one randomly selected instance of the process will have operating temperature greater than 93.8 Fahrenheit. (b) C is also normally distributed. Use the properties of E() and V AR() to find its mean and variance. (c) Find the probability that one randomly selected instance of the process will have operating temperature below 29 Celsius. (d) Find the Celsius temperature x such that the probability that the operating temperature in Celsius of one instance is less than x is .25.