A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws.
a. What is the probability that he will make more than 7 throws?
• enter your answer as a percent (56) or as a real-value (0.05)
. you enter your answer as a percent, you must use a-sign in your answer
• your answer must be accurate to the nearest whole percent.
b. How many baskets can the player expect to make it he takes 15 shots? .
. Your answers must be accurate to the nearest hundreth.
c. What is the standard deviation of the number of successful free throws out of 15 total?

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 [tex]\sqrt{(sample size)(probability)(1-probability)}[/tex]. Plugging in the numbers you get [tex]\sqrt{(15)(.7)(.3)}[/tex]=1.7748.