Statistic solve the problem.

Question

assume that when adults with smartphones are randomly​ selected,

53​%

use them in meetings or classes. If

5

adult smartphone users are randomly​ selected, find the probability that at least

2

of them use their smartphones in meetings or classes.

Answer 1

Use a binomial distribution since you are asking a yes-or-no question (binary response variable). You'll need to calculate the probability that exactly 2 of the five answer yes, then 3 of the five, 4 of the five, and 5 of the 5. Add up the individual probabilities for your answer. Alternatively, you may find the probabilities that exactly zero and exactly 1 answer yes and subtract the sum of P(0) and P(1) from 1 to get your answer.

P(2 yes in 5 people) = _nC_rp^rq^n-r, where p = proportion who answer yes in the population, and q = 1 - p. C is for combination of 5 people choose 2 yes. n = 5, r = 2, p = 0.53, q = 0.47.

P(2 yes in 5 people) = (5!/3!2!)*(0.53)²(0.47)³ = 0.2916

P(3 yes in 5 people) = 0.3289

P(4 yes in 5 people) = 0.1854

P(5 yes in 5 people) = 0.0418

P(X>=2, 5) = 0.8478 <--ANSWER