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Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made 80%of his field-goal attempts in the past. This season he attempts 20field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made 80%of his free-throw attempts in the past. This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

Short Answer

Expert verified

a) The distribution is not binomial

b) The distribution is binomial

Step by step solution

01

Part (a) Step 1: Given Information

A National Football League kicker has made 80%of his field-goal attempts in the past.

This season he attempts 20field goals.

The attempts differ widely in the distance, angle, wind, and so on.

02

Part (a) Step 2: Explanation

The binomial distribution will not be able to produce a decent approximation in this case because the attempts differ greatly in terms of angle, wind, distance, and other factors. As a result, the chances of success will vary depending on the attempt, resulting in draws.

03

Part (b) Step 1: Given Information 

A National Basketball Association player has made 80%of his free-throw attempts in the past.

This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

04

Part (b) Step 2: Explanation 

Because each consecutive draw is independent of the preceding draw, as success is called when a player makes a free throw, the variable X is a binomial distribution in this question. The total number of throws is set at 150. The chance of success is constant, i.e. 150 percent. Because each draw is considered independent, the same interference/distance holds true.

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