Question

Assume that when adults with smartphones are randomly​ selected, 58​% use them in meetings or classes. If 15 adult smartphone users are randomly​ selected, find the probability that exactly 10 of them use their smartphones in meetings or classes.

Answer 1

This problem is a case of binomial distribution. Let X be the no. of adults who use smartphones in meetings or classes, then the probability of success= p= 58% = 0.58

Now 15 users are randomly selected, thus selction of one user is independent of selection of another user. Also the no. of trials n= 15 is finite. Again, there are only two outcomes, success being that the selected adult uses the smartphone in meetings or classes and failure being that the selected adult doesn't use the smartphone in meetings or classes. Also the success probability p is constant for each trial.

Hence all the conditions of a binomial distribution are satisfied.

The PMF of X is given as

P(X=x) = 15Cx* (0.58)^(x) * (0.42)^(15-x) for x=0,1,2,...,15

Now we need to compute Prob.(Exactly 10 adults selected use their smartphones in meetings or classes) = P(X=10) = 15C10* (0.58)^10* (0.42)^5

= 0.16907590465, which is the required probability.