Question

Suppose that Charlie makes a free throw 0.82 on any one try. Assuming that this probability doesn’t change, find the chance that Charlie makes 4 out of the next seven free throws. Find the mean and standard deviation

Answer 1

Let $X=$ the number of successful throws: $X\sim Bin(n, p).$

Given $n=7, p=0.82, q=1-p=0.18.$

i)

$$P(X=4)=\dbinom{7}{4}(0.82)^4 (0.18)^{7-4}$$

$$=0.0922870936512$$

ii)

$$E(X)=np=7(0.82)=5.74$$

$$Var(x)=\sigma^2=npq=7(0.82)(0.18)=1.0332$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{1.0332}\approx1.016464$$