Question

Suppose that past history shows that 60% of college students prefer Coca-Cola ®. A sample of 10,000 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola ®?

a. Binomial distribution

b. Normal distribution

c. Poisson distribution

d. Exponential distribution

Answer 1

The distribution that should be used to figure out the probability that at least half of the selected students will prefer Coca-Cola is the binomial distribution.

Step-by-step explanation:

The distribution that should be used to figure out the probability that at least half of the selected students will prefer Coca-Cola is the binomial distribution.

In this case, we have a sample size of 10,000 students, and we are interested in the probability that at least half of them will prefer Coca-Cola. The binomial distribution is appropriate when we have a fixed number of independent trials (selecting each student) and each trial has only two possible outcomes (preferring or not preferring Coca-Cola).

The binomial probability can be calculated using the formula:

P(X ≥ k) = 1 - P(X < k) = 1 - Σi=0 to k-1 C(n, i) * pi * (1 - p)n-i,

where n is the sample size, p is the probability of preferring Coca-Cola, X is the number of students who prefer Coca-Cola, and k is the minimum number of students who prefer Coca-Cola that we are interested in.