Question

A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws.

Answer 1

Answer:

a.) .95

b.) The expected number of baskets is 10.50.

c.) 1.7748

Step-by-step explanation:

a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.

b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.

c.) The standard deviation of a binomial distribution can be calculated by the formula $\sqrt{(sample size)(probability)(1-probability)}$. Plugging in the numbers you get $\sqrt{(15)(.7)(.3)}$=1.7748.