Question

Say a business found that 98.3% of soda cans at a production facility in California are filled correctly. The company chooses 100 juice cans off the production line at that same facility. What assumption must be made for this study to follow the probabilities of a binomial experiment?

Answer 1

The events must be independent.

Explanation:

The only assumption that must be made is that the events are independent. That is, the amount of soda in a given can does not depend on the amount of soda of any previous can filled at the same facility.

If this assumption holds, then the probability of finding exactly k cans of soda filled correctly would be

`\displaystyle\binom{100}{k}(0.983)^k(1-0.983)^(100-k)`

where

`\displaystyle\binom{100}{k}=\displaystyle(100!)/(k!(n-k)!)`

are combinations of 100 elements taken k at a time.