Question

A baseball card collector buys and opens 360 packs of 1989 Fleer baseball cards. He is told that there is a 2.3% chance of anyone pack containing the coveted Billy Ripken error card. Find the mean and standard deviation of the random variable "number of Billy Ripken error cards ound", where n-360

Answer 1

Mean: 8.28

Standard deviation: 2.84

Explanation:

This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).

Then, the mean and standard deviation are calculate as for the binomial distribution:

`\mu=np=360\cdot 0.023=8.28\\\\\sigma=√(np(1-p))=√(360\cdot 0.023\cdot 0.977)=√(8.08956)\approx2.84`