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 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

A group of eight adult smartphone users was 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 eight.

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 eight trials should be equal to x=6.

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 six users who use their smartphones in meetings or classes is computed below:

$$\begin{gathered} P\left(X=6\right)={}^8{C}_6{\left(0.54\right)}^6{\left(0.46\right)}^{8-6} \\ =\frac{8!}{6!\left(8-6\right)!}{\left(0.54\right)}^6{\left(0.46\right)}^2 \\ =0.1469 \\ \approx 0.147 \end{gathered}$$

Therefore, the probability of getting six users who use their smartphones in meetings or classes is equal to 0.147.