From the time of early studies by Sir Francis Galton in the latenineteenth century linking it with mental ability, the cranialcapacity of the human skull has played an important role inarguments about IQ, racial differences, and evolution, sometimeswith serious consequences. (See, for example, S.J. Gould, \"TheMismeasure of Man,\" .) Suppose that the mean cranial capacitymeasurement for modern, adult males is cc (cubic centimeters) andthat the standard deviation is cc. Complete the followingstatements about the distribution of cranial capacity measurementsfor modern, adult males. (a) According to Chebyshev's theorem, atleast ? of the measurements lie between 565 cc and 1481 cc. (b)According to Chebyshev's theorem, at least 36% of the measurementslie between and . (Round your answer to the nearest integer.) (c)Suppose that the distribution is bell-shaped. According to theempirical rule, approximately 99.7% of the measurements lie betweenand . (d) Suppose that the distribution is bell-shaped. Accordingto the empirical rule, approximately ? of the measurements liebetween 565 cc and 1481 cc.
