Answer to Question #245738 in Statistics and Probability for clem

Question

Screws are sold in packets of 15. Faulty screws occur randomly. A large number of packets are tested for faulty screws and the mean number of faulty screws per packet is found to be 1.2. (i) Show that the variance of the number of faulty screws in a packet is 1.104

Answer 1

Let $X=$ the number of faulty screws in a packet: $X\sim Bin (n, p).$

Given $n=15.$

$$E(X)=np=15p=1.2=>p=0.08$$

$$q=1-p=1-0.08=0.92$$

$$Var(X)=\sigma^2=npq=15(0.08)(0.92)=1.104$$