Question

Assume that when adults with smartphones are randomly selected, 58% use them in meetings or classes. If 20 adult smartphone users are randomly selected, find the probability that exactly 13 of them use their smartphones in meetings or classes

Answer 1

0.1502 = 15.02% probability that exactly 13 of them use their smartphones in meetings or classes

Explanation:

For each adult smartphone users, there are only two possible outcomes. Either they use the phone in meetings or classes, or they do not. The probability of an adult using the phone in these settings is independent of any other adult. This 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) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

58% use them in meetings or classes

This means that
`p = 0.58`

20 adult smartphone users are randomly selected

This means that
`n = 20`

Find the probability that exactly 13 of them use their smartphones in meetings or classes.

This is
`P(X = 13)`. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 13) = C_(20,13).(0.58)^(13).(0.42)^(7) = 0.1502`

0.1502 = 15.02% probability that exactly 13 of them use their smartphones in meetings or classes