Suppose a recent poll shows that 50% of Americans drink soda every day. Amy, a researcher at a local university, takes a random sample of 16 Americans. Let X represent the number of Americans in Amy's sample who drink soda every day. Let μ and σ represent the parameters of a normal distribution and let n and p represent the parameters of a binomial distribution The sampling distribution of X is.

a. approximately normal with μ-0.5 and σ 0.125.
b. almost exactly binomial with n = 16 and p = 0.5.
c. exactly normal with μ 8 and σ = 2.000.
d. exactly binomial with n = 16 and p = 0.5.

d. exactly binomial with n = 16 and p = 0.5.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they drink soda, or they do not. The probability of an student drinking soda is independent of any other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

50% of Americans drink soda every day.

This means that

Random sample of 16 Americans.

This means that n = 16.

So the correct answer is:

d. exactly binomial with n = 16 and p = 0.5.

she will most likely have 33  

step-by-step explanation: