Let F be an RV that represents the operating temperature in Fahrenheit of one instance of a manufacturing process, and assume F ∼N(100, Var(F) = 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).

Using a Normal table, solve for the following:

(a) Find the probability that one randomly selected instance of the process will have operating temperature greater than 98.6 Fahrenheit.

(b) Find the distribution of C. (Hint: C ∼?(?, ?))

(c) Find the probability that one randomly selected instance of the process will have operating temperature below 32 Celsius.

(d) Above what temperature (in Celsius) is the top 10% of operating temperatures?

(e) Find the probability in a sample of 6 instances, more than 4 instances have operating temperature above 32 Celsius.(Assuming observations in the sample are independent)

(f) Find the distribution of C̅ for n=6, then find the probability that the average operating temperature in a sample of 6 instances is above 32 Celsius.