Question

Assume that when adults with smartphones are randomly​ selected, 46​% use them in meetings or classes. If 25 adult smartphone users are randomly​ selected, find the probability that exactly 19 of them use their smartphones in meetings or classes.

Answer 1

Let $X=$ the number of adults using their smartphones in meetings or classes: $X\sim Bin (n,p)$

$$P(X=x)=\dbinom{n}{x}p^x (1-p)^{n-x}$$

Given $n=25, p=0.46$

$$P(X=19)=\dbinom{25}{19}0.46^{19} (1-0.46)^{25-19}$$

$$=177100(0.46)^{19}(0.54)^6\approx0.001718$$