Final answer:
To find the probability that exactly 4 out of 36 people in a random sample are vegetarian, use the binomial probability formula.
Step-by-step explanation:
To find the probability that exactly 4 out of 36 people in a random sample are vegetarian, we can use the binomial probability formula. The formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the sample size (36), k is the number of successes (4), and p is the probability of success (0.034). Using this formula, we can calculate:
P(X=4) = (36 choose 4) * (0.034)^4 * (1-0.034)^(36-4)
Now, we can substitute the values into the formula and calculate the probability.
P(X=4) = (36!)/((4!)(36-4)!) * (0.034)^4 * (1-0.034)^(36-4)
Calculating this equation will give us the probability that exactly 4 out of 36 people in a random sample are vegetarian.