In Exercises 21–24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).

If 20 adult smartphone users are randomly selected, find the probability that exactly 15 of them use their smartphones in meetings or classes.

A group of 20 adult smartphone users is selected. The probability of selecting a user who uses his/her smartphone in meetings or classes is equal to 0.54.

Let X denote the users who use their smartphones in meetings or classes.

Let success be defined as selecting a user who uses his/her smartphone in meetings or classes.

The number of trials (n) is given to be equal to 20.

The probability of success is calculated below:

$$\begin{gathered} p=54\% \\ =\frac{54}{100} \\ =0.54 \end{gathered}$$

The probability of failure is calculated below:

$$\begin{gathered} q=1-p \\ =1-0.54 \\ =0.46 \end{gathered}$$

The number of successes required in 20 trials should be equal to x=15.

The binomial probability formula is as follows:

$P\left(X=x\right)={}^n{C}_x{\left(p\right)}^x{\left(q\right)}^{n-x}$

By using the binomial probability formula, the probability of getting 15 users who use their smartphones in meetings or classes is computed below:

$$\begin{gathered} P\left(X=15\right)={}^{20}{C}_{15}{\left(0.54\right)}^{15}{\left(0.46\right)}^{20-15} \\ =\frac{20!}{15!\left(20-15\right)!}{\left(0.54\right)}^{15}{\left(0.46\right)}^5 \\ =0.0309 \\ \approx 0.031 \end{gathered}$$

Therefore, the probability of getting 15 users who use their smartphones in meetings or classes is equal to 0.031.