In the Exercise, Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape.8 Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 98.6 degrees and a standard deviation of 0.8 degrees.

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

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

Exercise:

What’s Normal? 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, and Levine21 took temperatures from 148 healthy people over a three-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.²²Â The body temperatures for these 130 individuals are shown in the relative frequency histogram that follows.

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x =----------- 98-----------.25----------- µ----------- = -----------98.-----------6 s----------- = -----------0.8----------- n -----------=13-----------0 s-----------amp-----------le -----------s =----------- 0.-----------8/s-----------qrt-----------(13-----------0) -----------=0.-----------07 -----------a) -----------The----------- pr-----------oba-----------bil-----------ity----------- th-----------at -----------the----------- av-----------era-----------ge -----------tem-----------per-----------atu-----------re -----------for----------- 13-----------0 p-----------eop-----------le -----------is -----------98.-----------25 -----------deg-----------ree-----------s o-----------r l-----------owe-----------r

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