30 May Math
From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences. (See, for example, S.J. Gould, “The Mismeasure of Man,” 1996.)
Suppose that the mean cranial capacity measurement for modern, adult males is
1041 cc (cubic centimeters).
Complete the following statements about the distribution of cranial capacity measurements for modern, adult males.
(a) According to Chebyshev’s theorem, at least ?56%75%84%89% of the measurements lie within 2 standard deviations of the mean, 1041cc.
(b) Suppose that the distribution is bell-shaped. If approximately 99.7% of the measurements lie between 309 cc and 1773 cc, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .
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