consider caleb the basketball player. In a game, he shoots 10 free throws. In the year, he makes 70% of his free throws. Is this a binomial setting? Fully explain your response.
p(good) = .7 , p(fail) = .3
n = 10
crunch it out with your binomial distribution
P(2) for example = C(10,2)*.7^2*.3^8
= 10!/[8!*2!] * .49 * 6.56*10^-5
= 45 * .49 * 6.56*10^-5
= .001447
thanks
You are welcome :)
To determine whether this situation is a binomial setting, we need to consider the conditions that define a binomial experiment.
1. There should be a fixed number of trials: Yes, we know that Caleb shoots exactly 10 free throws.
2. Each trial should have only two outcomes: In this case, Caleb either makes a free throw or misses it. So, there are two possible outcomes.
3. The probability of success remains constant for each trial: We are given that Caleb makes 70% of his free throws throughout the year. Therefore, the probability of success (making a free throw) does remain constant for each trial.
4. The trials are independent of each other: This condition means that the outcome of one trial should not affect the outcome of another trial. In this case, we assume that each free throw Caleb takes is independent of the others. The outcome of one free throw does not depend on the outcome of another.
Based on the above conditions, we can conclude that this situation does indeed meet the criteria for a binomial setting.