Based on data collected by the National Center for Health Statistics and made available to the public in the Sample Adult database, an estimate of the percentage of adults who have at some point in their life been told they have hypertension is 23.53 percent. If we select a simple random sample of 20 U.S. adults and assume that the probability that each has been told that he or she has hypertension is .24, find the probability that the number of people in the sample who have been told that they have hypertension will be exactly 3?
P(x) = (nCx)(p^x)[q^(n-x)]
x = 3
n = 20
p = .24
q = 1 - p
(nCx) this is the part that I can not finger out
To calculate the probability that the number of people in the sample who have been told they have hypertension is exactly 3, you can use the binomial probability formula.
Let's break down the formula and calculate each part separately:
P(x) = (nCx)(p^x)(q^(n-x))
Here, P(x) represents the probability that exactly x people in the sample have been told they have hypertension.
nCx represents the number of combinations of selecting x objects from a set of n objects. To calculate this value, you can use the formula:
nCx = n! / (x!(n-x)!)
Using this formula:
n = 20 (total sample size)
x = 3 (number of people who have been told they have hypertension)
nCx = 20! / (3!(20-3)!) = 20! / (3!17!)
Now we need to calculate p^x and q^(n-x):
p = 0.24 (probability that each person has been told they have hypertension)
q = 1 - p = 1 - 0.24 = 0.76 (probability that each person has not been told they have hypertension)
p^x = 0.24^3 = 0.013824
q^(n-x) = 0.76^(20-3) = 0.000445676
Now we can plug these values into the formula to calculate the probability:
P(3) = (20 choose 3) * (0.24^3) * (0.76^(20-3))
P(3) = (20! / (3!17!)) * (0.013824) * (0.000445676)
Using a calculator or statistical software, you can input these values to find the final probability.