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 (32∘F,(32∘F, or 0∘C0∘C ) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50∘F50∘F . The manufacturer claims that the thermostat allows variation in home temperature that follows a Normal distribution with σ=3∘Fσ=3∘F . To test this claim, Mrs. Starnes programs her digital thermometer to take an SRS of n=10n=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 μ=50∘Fμ=50∘F and standard deviation σ=3∘Fσ=3∘F Cold cabin? The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that's N(50,3)N(50,3) and recording the sample variance s2xsx2 each time. (a) Describe the approximate sampling distribution. (b) Suppose that the variance from an actual sample is s2x=25.sx2=25. What would you conclude about the thermostat manufacturer's claim? Explain.