Final answer:
In order to find the probability that exactly 3 out of 20 randomly selected people in the area own a dog, we can use the binomial probability formula. In this case, n is 20, k is 3, p is 0.36. The probability is approximately 0.1637.
Step-by-step explanation:
In order to find the probability that exactly 3 out of 20 randomly selected people in the area own a dog, we can use the binomial probability formula.
The formula is: P(X = k) = nCk * p^k * (1-p)^(n-k)
where n is the total number of trials, k is the number of successful trials, p is the probability of success, and nCk is the number of combinations.
In this case, n is 20, k is 3, p is 0.36, and nCk is calculated as 20C3 = 1140.
Plugging these values into the formula:
P(X = 3) = 1140 * (0.36)^3 * (1-0.36)^(20-3) ≈ 0.1637
Therefore, the probability that exactly 3 out of 20 randomly selected people in the area own a dog is approximately 0.1637.
Complete Question:
In a certain area, 36% of people own a dog. Find the probability that exactly 3 out of 20 randomly selected people in the area own a dog. For this p= 0.36.