Question

Assume this year's flu vaccine has a 75% chance of being effective. If the vaccine is given to 304 randomly selected people, answer the following. d) What is the probability that exactly 232 of them do not respond to the vaccine?

Answer 1

To find the probability that exactly 232 of the 304 people do not respond to the vaccine, use the binomial probability formula with the given values of n, k, and p.

Step-by-step explanation:

To find the probability that exactly 232 of the 304 people do not respond to the vaccine, we need to use the binomial probability formula.

The formula is:

P(X=k) = C(n, k) * pk * (1-p)(n-k)

In this formula, P(X=k) represents the probability of exactly k successes, n is the number of trials, p is the probability of success, and C(n, k) represents the combination of n items taken k at a time.

Using the given information, we have:

n = 304 (number of trials)

k = 232 (number of successes)

p = 0.25 (probability of success)

Plugging in these values into the formula:

P(X=232) = C(304, 232) * 0.25232 * (1-0.25)(304-232)

You can use a calculator or a statistical software to calculate the combination and exponentiation.