5. An actual scenario using the sampling distribution of the sample mean . Different people have slightly different body temperatures, so that what is considered normal body temperature is of course only an average. Normal body temperature is traditionally assumed to be 98.6F. This number origi- nates from a German study in 1868 by Carl Wunderlich, who reported a temperature of 37 Celsius to be typical. Converting Celsius to Fahrenheit gives the traditionally- assumed value of 98.6. But Wunderlichs value was only accurate to the nearest degree; so the extra point-six in the traditionally-assumed value of 98.6 is not a justified digit of accuracy. So, the question arises as to whether the true population mean body temperature really is the traditionally-assumed value of = 98.6F. An actual modern study of a random sample of n = 700 body temperature readings found a sample mean temperature of 98.2F. [Note, this is real data.] For the purpose of this exercise, assume the true population standard deviation of body temperature is = 0.7F (this assumption is consistent with many studies). = The question here is whether the observed result of 98.2F could have happened just by chance due to the natural sampling variability of X, or is this result unusually low and thus provides evidence against the assumed value of : 98.6F. To answer this question we need to determine the sampling distribution of X in this case and see which values are reasonable and which values are unusual. - (a) Assuming = 98.6F and = 0.7F, what is the sampling distribution of X, the average body temperature of a random sample of n = 700 humans? Be sure to mention: the shape of the distribution (and justify it), the mean () and, the standard deviation (%) [round to 3 decimal digits].