Answer:
Explanation:
To find the probability that 3 or fewer adults out of 13 randomly selected adults report that their health is excellent, we can use a binomial probability formula. This formula is used to calculate the probability of a specific number of successes in a set number of independent trials, given a certain probability of success in each trial.
In this case, the probability of success is the probability that an individual adult reports that their health is excellent, which is 39%. The number of trials is 13, and the number of successes we want to consider is 3 or fewer.
Using the binomial probability formula, we can calculate the probability as follows:
P(X ≤ 3) = (13 choose 0) * (0.39)^0 * (1 - 0.39)^13 + (13 choose 1) * (0.39)^1 * (1 - 0.39)^12 + (13 choose 2) * (0.39)^2 * (1 - 0.39)^11 + (13 choose 3) * (0.39)^3 * (1 - 0.39)^10
Plugging in the values, we get:
P(X ≤ 3) = 1 * (1 - 0.39)^13 + 13 * (0.39) * (1 - 0.39)^12 + 78 * (0.39)^2 * (1 - 0.39)^11 + 286 * (0.39)^3 * (1 - 0.39)^10
Calculating this out, we get a probability of P(X ≤ 3) = 0.2968
Therefore, the probability that 3 or fewer adults out of 13 randomly selected adults report that their health is excellent is approximately 0.2968.
I hope this helps! Let me know if you have any questions.