Answer to Question #220905 in Statistics and Probability for bbdel

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 4 of them use their smartphones in meetings or classes.

Answer 1

Let X be a random variable denoting the number of adults out of a randomly selected 9 people, who use their smartphones in meetings or classes. X has Binomial distribution with parameters $n=9$, $p=0.44$. This means that the probability that exactly $k$ adults use their smartphones in meetings or classes is equal to $P(X=k)=\binom{k}{n}p^k(1-p)^{n-k}$.

Therefore, $P(X=4)=\frac{9!}{4!5!}0.46^4\cdot0.54^5=0.259$.