Normal Temperatures In Exercise 1.67, Allen Shoemaker derived a distribution of huma...

Normal Temperatures In Exercise 1.67, Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape.9 Suppose we assume that the temperatures of healthy humans are approximately normal with a mean of 98.6° and a standard deviation of 0.8.

a. If 130 healthy people are selected at random, what is the probability that the average temperature for these people is 98.25° or lower?

b. Would you consider an average temperature of 98.25° to be an unlikely occurrence, given that the true average temperature of healthy people is 98.6°? Explain.

Reference:

p> What’s Normal? The 98.6 degree standard for human body temperature was derived by a German doctor in 1868. In an attempt to verify his claim, Mackowiak, Wasserman, andLevine22 took temperatures from 148 healthy people over a 3-day period. A data set closely matching the one in Mackowiak’s article was derived by Allen Shoemaker, and appears in the Journal of Statistics Education.23 The body temperatures for these 130 individuals are shown in the relative frequency histogram that follows.

a. Describe the shape of the distribution of temperatures.

b. Are there any unusual observations? Can you think of any explanation for these?

c. Locate the 98.6-degree standard on the horizontal axis of the graph. Does it appear to be near the center of the distribution?