Question

Assume that when adults with smartphones are randomly​ selected, 46​% use them in meetings or classes. If 9 adult smartphone users are randomly​ selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.

Answer 1

0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.

Explanation:

We are given the following information:

We treat adult using smartphones in meetings or classes as a success.

P(Adult using smartphone) = 46% = 0.46

Then the number of adults follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 9

We have to evaluate:

`P(x = 3)\\\\= \binom{9}{3}(0.46)^3(1-0.46)^6\\\\= 0.2027`

0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.