Question

A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n

Answer 1

Answer:

The value of n is 7.

Step-by-step explanation:

For each teen, there are only two possible outcomes. Either they buy soda at least once each week, or they do not. Since they were selected randomly, the teens are independent of each other, which means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In the binomial distribution, we have that n is the size of the sample. In this question, seven teens are randomly selected, which means that the value of n is 7.