7.39 Normal Temperatures In Exercise 1.68, Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape.10 Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 37 Celsius and a standard deviation of 0.2 degrees.

a. If 130 healthy people are selected at random, what is the probability that the average temperature for these people is 36.81C or lower?

b. Would you consider an average temperature of 36.81C to be an unlikely occurrence, given that the true average temperature of healthy people is 37C? Explain.