Question

II. We learned in Exercise 3.25 that about 70% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. (a) How many people would you expect to have consumed alcoholic beverages

Answer 1

You would expect for 35 people to have consumed alcoholic beverages.

Explanation:

For each person, there are only two possible outcomes. Either they consumed alcoholic beverages, or they did not. The probability of a person having consumed alcoholic beverage is independent of any other person. This 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`

We learned in Exercise 3.25 that about 70% of 18-20 year olds consumed alcoholic beverages in 2008.

This means that
`p = 0.7`

We now consider a random sample of fifty 18-20 year olds.

This means that
`n = 50`

How many people would you expect to have consumed alcoholic beverages

`E(X) = np = 50*0.7 = 35`

You would expect for 35 people to have consumed alcoholic beverages.