48. Body temperatures Most people think that the adult body temperature is 98.6°

Question

48. Body temperatures Most people think that the adult body temperature is 98.6°F. That figure, banormal" a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be 98.2°F. Furthermore, the standard devia- tion appeared to be around 0.7°F. Assume that a Normal model is appropriate. based on a) In what interval would you expect most people's body temperatures to be? Explain body temperatures above 98.6°E? all people? b) What fraction of people would be expected to have c) Below what body temperature are the coolest 20% of

Explanation / Answer

48)

a.The interval will give the range of temperatures where we might expect the true temperature to
lie between

So, Interval = Mean +/- Z*Stdev = 98.2 +/- 1.96*.7 = 96.828 to 99.572

This is assuming that we have to find 95% Ci, as no info on the confidence level has been mentioned.
We always assume it be 95% when nothing in given in the question.

b. P(X>98.6) = P(Z> (98.6-98.2)/.7) = P(Z> .6/.7) = 1-.80432 = .19568

So, 19.57% fraction of people would be expected to have temp. above 98.6 F

c.

P(X<=c) = .20
Z = -.845
So, c = Z*Stdev + Mean = -.845*.7+98.2 = 97.6085
Hence, Below 97.6085 F are the coolest 20% of all people

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