The respiratory disease emphysema, which is most commonly caused by smoking, causes damage to the air sacs in the lungs. According to the National Center for Health Statistics report Data from the National Health Interview Survey, 1.5% of the adult American population suffer from emphysema. Of 100 randomly selected adult Americans, let X denote the number who have emphysema.
a. What are the parameters for the appropriate binomial distribution?
b. What is the parameter for the approximating Poisson distribution?
c. Compute the individual probabilities for the binomial distribution in part (a). Obtain the probabilities until they are zero to four decimal places.
d. Compute the individual probabilities for the Poisson distribution in part (b). Obtain the probabilities until they are zero to four decimal places.
e. Compare the probabilities that you obtained in parts (c) and (d).