Question

. (10 pts.) According to the National Institute of Allergy and Infectious Diseases, about 4.2% of American adults have a food allergy. A large company plans a lunch reception for its 350 employees. Assume that employees are independent. Let the random variable X be the number of company employees who have a food allergy.

(a) What is the distribution of X?

(b) What are the mean and standard deviation of the distribution of X?

(c) Using the Normal approximation (with continuity correction), determine the probability that at most 20 of the 350 employees have a food allergy.

SHOW WORK AND EXPLAIN

Answer 1

a ) Given , X : number of company employees who have a food allergy.

Probability that an American adult has food allergy = 0.042

Thus X follows a binomial distribution with parameters n = 350 and p = 0.042

b )  

c ) Now , and

Thus ,

( Using continuity correction )