Question

In a bowling game, there are 10 pins each round. The games mix beginner and experts, so we assume the pmf of the # of pins knocked over per round is symmetric. Suppose the mean of pmf is 5.7 pins, sd of pmf is 1.9 pins, and the results of each round are independent. What’s the probability that I knocked over 200 pins when I play 31 times?

* assume you can bowls 1 times each round.( play 31 times means bowls 31 rounds.) *

Answer 1

$Let~X_i~denote~the~no.~of~pins~are~knocked~at~ith~round,~i=1(1)10.\\ Then~Y=\sum_{i=1}^{31}X_i\overset{a}{\rightarrow}Normal(5.7*31,~1.9^2*31)~(using~Central~limit~theorem)\\ P(Y>200)=1-\Phi((200-5.7*31)/\sqrt{1.9^2*31})=0.0138$