Question

Assume that when adults with smartphones are randomly​ selected, 45​% use them in meetings or classes. If 30 adult smartphone users are randomly​ selected, find the probability that exactly 24 of them use their smartphones in meetings or classes.

Answer 1

This problem involves a binomial distribution with n = 30 trials and a success probability of p = 0.45 (using a smartphone in meetings or classes).

The probability of exactly k successes in n trials is given by the binomial probability formula:

P(k successes) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, equal to n! / (k! * (n - k)!).

Substituting n = 30, p = 0.45, and k = 24, we have:

P(24 out of 30 use smartphones in meetings/classes) = (30 choose 24) * (0.45)^24 * (0.55)^6

Using a calculator or software, we can evaluate this probability as:

P(24 out of 30 use smartphones in meetings/classes) ≈ 0.005

Therefore, the probability of exactly 24 out of 30 adult smartphone users using their smartphones in meetings or classes, when randomly selected, is approximately 0.005 or 0.5%.