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. 10.5

c. 1.77

Explanation:

To find the probability that x shots are successful from n trials, we will use the following equation for the binomial distribution

$\begin{gathered} P(x)=nCx\cdot p^x\cdot(1-p)^{n-x} \\ \text{ Where nCx = }\frac{n!}{x!(n-x)!} \end{gathered}$

In this case, n = 15 free throws, p = 70% which is the probability of success, and we need to calculate the probability that he will make more than 7 throws, so x > 7. Then, the probability is equal to

$\begin{gathered} P(x>7)=P(8)+P(9)+P(10)+P(11)+...+P(15) \\ P(x>7)=\sum_{x\mathop{=}8}^{15}15Cx\cdot0.7^x\cdot(1-0.7)^{15-x} \\ \\ P(x>7)=0.95=95\text{ \%} \end{gathered}$

Additionally, the expected value and the standard deviation for a binomial probability are equal to

$\begin{gathered} E(x)=np \\ S(x)=\sqrt{np(1-p)} \end{gathered}$

So, replacing n = 15, and p = 0.7, we get:

$\begin{gathered} E(x)=15(0.7)=10.5 \\ S(x)=\sqrt{15(0.7)(1-0.7)}=1.77 \end{gathered}$

Therefore, the answers are

a. 95%

b. 10.5

c. 1.77