Solved: Exercises 13 and 14 refer to the following setting. During the winter months

QUESTION:

Exercises 13 and 14 refer to the following setting. During the winter months, outside temperatures at the Starneses cabin in Colorado can stay well below freezing (32F, or 0C) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50F. The manufacturer claims that the thermostat allows variation in home temperature that follows a Normal distribution with s = 3F. To test this claim, Mrs. Starnes programs her digital thermometer to take an SRS of n = 10 readings during a 24-hour period. Suppose the thermostat is working properly and that the actual temperatures in the cabin vary according to a Normal distribution with mean m = 50F and standard deviation s = 3F. Cold cabin? The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3) and recording the sample minimum each time. Sample minimum (a) Describe the approximate sampling distribution. (b) Suppose that the minimum of an actual sample is 40F. What would you conclude about the thermostat manufacturers claim? Explain.