Question

Postpartum depression and anxiety (PPD), is a common medical condition affecting mothers and their families after the birth of a baby. The CDC estimated that 17% of women who have recently given birth experience symptoms of PPD. If 100 women who recently gave birth are randomly selected, what is the probability that at least 20 of them experience symptoms of PPD?

Answer 1

To find the probability that at least 20 of the randomly selected women experience symptoms of PPD, we can use the binomial probability formula. The probability is approximately 10.44%.

Step-by-step explanation:

To find the probability that at least 20 of the randomly selected women experience symptoms of postpartum depression and anxiety (PPD), we can use the binomial probability formula.

The formula is P(X >= k) = 1 - P(X < k-1), where X is a binomial random variable representing the number of women experiencing symptoms of PPD, k is the minimum number of women we want to calculate the probability for, and P(X < k-1) is the cumulative probability of getting less than (k-1) successes.

In this case, we want to find the probability that at least 20 out of 100 women experience symptoms of PPD.

Since the probability for each woman is 17%, we can calculate P(X < 20) and subtract it from 1 to find P(X >= 20).

Using a binomial distribution calculator or software, we can find that P(X < 20) is approximately 0.8956.

Therefore, P(X >= 20) = 1 - 0.8956 = 0.1044, or approximately 10.44%.