based on data collected by national center for health statistics and made a public in the sample adult database (A-5) sn estimate of the percentage of adults some point in their life been told they have hypertension is 23.53 percent if we set random sample of 20 U.S adults and assume that the probability that each has been or she has hypertension is.24 find the probability that the number of people in the have been told that they have hypertension will be: (a) exactly three (b) three or more (c) fewer than three (d) Between three and seven, inclusive

What is 20 times .24?

To find the probability of these scenarios, we will use the binomial probability formula. The formula for the probability of getting exactly "k" successes in "n" trials, given the probability of success in a single trial "p" is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where (n choose k) denotes the number of ways to choose k elements from a set of size n, and ^ denotes exponentiation.

(a) To find the probability of exactly three people having been told they have hypertension, we will use the values n = 20, k = 3, and p = 0.24.

P(X = 3) = (20 choose 3) * (0.24^3) * (1 - 0.24)^(20 - 3)

(b) To find the probability of three or more people having been told they have hypertension, we need to sum the probabilities of exactly three, four, five, ..., up to 20. This can be done as follows:

P(X >= 3) = P(X = 3) + P(X = 4) + ... + P(X = 20)

(c) To find the probability of fewer than three people having been told they have hypertension, we need to find the complement of the probability of three or more people. This can be calculated as:

P(X < 3) = 1 - P(X >= 3)

(d) To find the probability of between three and seven people (inclusive) having been told they have hypertension, we need to sum the probabilities of exactly three, four, five, six, and seven. This can be calculated as:

P(3 <= X <= 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Using these formulas, you can calculate the probabilities based on the given values of n, k, and p.