The probability that a randomly selected individual in a certain community has made an online purchase is 0.40 . Suppose that a sample of 13 people from the community is selected, what is the probability that at most 3 of them has made an online purchase?
Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage.
.093
To find the probability that at most 3 people have made an online purchase, you can use the binomial probability formula.
The binomial probability formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
- P(X = k) is the probability of getting exactly k successes
- C(n, k) is the number of combinations of n things taken k at a time
- p is the probability of success on a single trial
- n is the number of trials
In this case, we want to find the probability that at most 3 out of the 13 people have made an online purchase. This includes the probabilities of having exactly 0, 1, 2, or 3 successes.
Let's calculate each of these probabilities individually and sum them up:
P(X = 0) = C(13, 0) * (0.40)^0 * (1 - 0.40)^(13 - 0)
P(X = 1) = C(13, 1) * (0.40)^1 * (1 - 0.40)^(13 - 1)
P(X = 2) = C(13, 2) * (0.40)^2 * (1 - 0.40)^(13 - 2)
P(X = 3) = C(13, 3) * (0.40)^3 * (1 - 0.40)^(13 - 3)
Now, add up these probabilities to get the final answer:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Simply plug in the values and calculate each term using a calculator or a statistical software to obtain the final answer. Make sure to round the probability to 2 decimal places as requested.