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 $20$field 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 $150$free throws. Basketball free throws are always attempted from $15$feet away with no interference from other players

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

This season he attempts $20$field goals.

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

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.

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

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

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.