Question: Too cool at the cabin? During the winter months, the temperatures at the Starneses' Colorado cabin can stay well below freezing (32°F or 0°C) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50°F. She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature T in the cabin at midnight on a randomly selected night follows a Normal distribution with mean 8.5°C and standard deviation 2.25°C.
(a) Let Y = the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that F = (9/5)C + 32). Find the mean and standard deviation of Y.
(b) Find the probability that the midnight temperature in the cabin is below 40°F. Show your work.