From the time of early studies by Sir Francis Galton in the late nineteenth century linking...

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," .) Suppose that the mean cranial capacity measurement for modern, adult males is cc (cubic centimeters) and that the standard deviation is cc. Complete the following statements about the distribution of cranial capacity measurements for modern, adult males. (a) According to Chebyshev's theorem, at least ? of the measurements lie between 565 cc and 1481 cc. (b) According to Chebyshev's theorem, at least 36% of the measurements lie between and . (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 between and . (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ? of the measurements lie between 565 cc and 1481 cc.

Expert Solution

a) 1 - 1/k² = 0.36

or, 1/k² = 0.64

or, k² = 1/0.64

or, k = 1.25

1096 - 1.25 * 269 = 759.75

1096 + 1.25 * 269 = 1432.25

According to Chebyshev's theorem, at least 36% of measurements lie between 759.75 cc and 1432.25 cc.

b) 1096 - 2 * 269 = 558

1096 + 2 * 269 = 1634

Here, k = 2

1 - 1/k²

= 1 - 1/2²

= 1 - 1/4

= 3/4 = 0.75 = 75%

According to Chebyshev's theorem, at least 75% of measurements lie between 558 cc and 1634 cc.

c) According to empirical rule about 95% of the data fall within two standard deviation from the mean.

Approximately 95% of the measurements lie between 558 cc and 1634 cc.

d) According to empirical rule about 99.7% of the data fall within three standard deviation from the mean.

1096 - 3 * 269 = 289

1096 + 3 * 269 = 1903

Approximately 99.7% of the measurements lie between 289 cc and 1903 cc.

HOPE YOU LIKE IT.

IF YOU HAVE ANY DOUBT, FEEL FREE TO ASK IT IN THE COMMENT SECTION.

THANK YOU.

Colby Messinger answered 1 year ago

Compare and contrast the second industrial revolution (late nineteenth century to the early twentieth century) to the first industrial revolution (late eighteenth century to the early nineteenth century)

Compare and contrast the second industrial revolution (late nineteenth century to the early twentieth century) to the first industrial revolution (late eighteenth century to the early nineteenth century).

Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of...

Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest (adult) son. The...

compare and contrast globalization as it existed in the late nineteenth century with globalization today

What is the connection between the new imperialism of the late nineteenth century and the causes...

What is the connection between the new imperialism of the late nineteenth century and the causes of World War I?

Discuss how the United States was perceived as a world power in the late nineteenth century...

Discuss how the United States was perceived as a world power in the late nineteenth century and the changes that occurred concerning its foreign policy.

America’s Gilded Age in the late nineteenth century began with a raft of innovations – railroads,...

America’s Gilded Age in the late nineteenth century began with a raft of innovations – railroads, steel production, oil extraction – but culminated in mammoth trusts owned by “robber barons” who used their wealth and power to drive out competitors, and then to corrupt American politics. We are now in a second Gilded Age – ushered in by semiconductors, software, and the Internet – and a handful of technology giants are the new robber barons. Facebook and Google now dominate...

Question

From the time of early studies by Sir Francis Galton in the late nineteenth century linking...

Solutions

Expert Solution

Related Solutions

Compare and contrast the second industrial revolution (late nineteenth century to the early twentieth century) to the first industrial revolution (late eighteenth century to the early nineteenth century)

Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of...

compare and contrast globalization as it existed in the late nineteenth century with globalization today

What is the connection between the new imperialism of the late nineteenth century and the causes...

Discuss how the United States was perceived as a world power in the late nineteenth century...

America’s Gilded Age in the late nineteenth century began with a raft of innovations – railroads,...

Discuss the extent to which US policy in Latin America in the late-nineteenth century and the...

In the early nineteenth century, Americans strove to resolve their political disputes through compromise, yet by...

What were the main social, political, and economic factors in the early nineteenth century that encouraged...

What significant political and legal reforms did the Russian government implement in the late nineteenth century?...