State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York.
Which distribution does X follow?

Question

Quizplus · Accepted Answer

X follows a binomial distribution with n=20 (sample size) and p=0.145 (probability of success, i.e. being obese). The mean of a binomial distribution is given by np, which in this case is 20 x 0.145 = 2.9. Therefore, the correct choice is D. The Poisson distribution is not appropriate here since the sample size is not very large and the probability of success is not very small.

State-Wide Surveys Indicate That 14