Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. (Of course, they are in the end defeated by the hero and heroine.) Biologists use power functions as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed to "radiation," is enlarged to 300 times its normal length. (Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction.) (a) By how much will its weight be increased? Its weight is increased by a factor of (300 (b) By how much will the cross-sectional area of its legs be increased? The cross-sectional area of its legs is increased by a factor of (4000 (c) Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? Note: The factor by which pressure increases is given by Factor of increase in weight Factor of increase in area The pressure on a leg increases by a factor of (200

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A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.