In each of the following exercises, assume that N is sufficiently large relative

Question

In each of the following exercises, assume that N is sufficiently large relative to n that the binomial distribution may be used to find the desired probabilities. Based on data collected by the National Center for Health Statistics and made available to the public in the Sample Adult database (A - 5), an estimate of the percentage of adults who have at some point in their life been told they have hypertension is23.53 percent. If we select a simpler 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: (a) Exactly three (b) Three or more (c) Fewer than three (d) Between three and seven, inclusive

Explanation / Answer

Probability of having hypertension for each person is = 0.24.

Hence out of 20 persons, Let X be the number of persons having hypertension. Then X~Bin(20,0.24).

Hence, E(X) = 20 * 0.24 = 4.8.

So the number of persons will be between 3 and 7. Hence Option (D) is the cotrrect choice.

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