Question

Assume that when adults with smartphones are randomly selected, 58% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find theprobability that exactly 3 of them use their smartphones in meetings or classesThe probability is a

Answer 1

This is a binomial probability distribution question.

The binomial probability formula is >>>

$P(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}_{}$

Where

n is the number of trials (number being sampled)

x is the number of success desired

p is the probability of getting a success

q = 1 - p is the probability of failure

From the given problem,

n = 6

x = 3

p = 58% = 0.58

q = 1 - p = 1 - 0.58 = 0.42

Substituting into the formula, we find the probability that exactly 3 of the people use smartphone in meetings or classes:

$\begin{gathered} P(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}_{} \\ P(x=3)=\frac{6!}{(6-3)!3!}(0.58)^3(0.42)^{6-3}_{} \\ =\frac{6!}{3!3!}(0.58)^3(0.42)^3 \\ =0.2891 \end{gathered}$