Question

Suppose that the probability that a person will develop hypertension over a life time is 60%. Of 13 graduating students from the same college are selected at random. find the mean number of the students who develop hypertension over a life time

Answer 1

The mean number of the students who develop hypertension over a life time is 7.8.

Explanation:

For each person, there are only two possible outcomes, either they will develop hypertension, or they will not. The probability of a person developing hypertension is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

Suppose that the probability that a person will develop hypertension over a life time is 60%.

This means that
`p = 0.6`

13 graduating students from the same college are selected at random.

This means that
`n = 13`

Find the mean number of the students who develop hypertension over a life time

`E(X) = np = 13*0.6 = 7.8`

The mean number of the students who develop hypertension over a life time is 7.8.