Exam 11: Discrete Probability Distributions

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent. A researcher suggests using 500 births instead of only 5. In this case, which distribution is a reasonable approximation of X?

According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 8 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy. What are the approximate values of the mean and standard deviation of the distribution of X?

According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 8 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy. What is the probability P(X < 2)?