Question 1 Assume 20% of a population prefers cereal A to cereal B. We interview 100 randomly selected individuals.

a) What probability distribution can be used to model the random variable X, the number of people in the sample of 100 individuals who prefer cereal A to cereal B? Give the values of the parameters in the model. Answer:

b) What is the expected number of people who prefer cereal A to cereal B? Compute E[X]. Answer:

c) What is the variance of the number of people who prefer cereal A to cereal B? Compute V (X). Answer:

d) Use normal approximation to estimate the probability that at least 25 people in the sample prefer cereal A to cereal B.