Answer to Question #267930 in Statistics and Probability for Sadie

Question

The number of attempts at shooting goals made by a netballer in a tournament can be modelled by a binomial distribution with a probability of success equal to 0.35.

(i) In a sample of 12 attempts at shooting goals, calculate the probability that EXACTLY 4 were successful.

(ii) Given that the netballer made a total of 120 attempts at shooting goals in a tournament, calculate the expected number of successful shoots. 

Answer 1

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

Given $p=0.35, q=1-p=0.65$

(i) $n=12$

$$P(X=4)=\dbinom{12}{4}(0.25)^4(0.65)^{12-4}$$

$$\approx0.23669235431$$

(ii) $n=120$

$$E(X)=np=120(0.35)=42$$