According to study done by Nick Wilson of Otago University, the probabilitya randomly selected individual will not cover his or her mouth when sneezing was 0.267. Suppose you sit on a mall bench and observe 200 people pass by as they sneeze.
1) Use the normal approximation to the binomialto find the probability of observing less than 40 people that don’t cover while sneezing.
2) Find the actual probability of observing less than 40 people that don’t cover their nose while sneezing using the binomial. How close are the two probabilities?
This solution provides a step-by-step solution to using the normal approximation for finding probabilities.