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

1017

cc (cubic centimeters) and that the standard deviation is255

cc. 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 between 507 cc and 1527cc.

(b) According to Chebyshev's theorem, at least 36% of the measurements lie betweencc

andcc

. (Round your answer to the nearest integer.)

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the measurements lie betweencc

andcc

.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately?

68%

75%

95%

99.7%

of the measurements lie between 507 cc and 1527cc.