Question

Assume that when adults with smartphones are randomly selected, 43% use them in meetings or classes. 17 at smartphone users are randomly selected, findprobability that exactly 2 of them use their smartphones in meetings or classes.

Answer 1

Binomial Distribution

The probability that a random adult with smartphones uses them in meetings or classes is p=43%, or p=0.43 when expressed as a decimal.

The probability that the selected adult is not using them in classes is q = 1 - p = 0.57.

The binomial distribution is used when two possible outcomes are expected from a repeating random experience.

In our case, the total number of experiments is n=17 and we want to compute the probability that exactly m=2 of them is successful. The formula is:

`P=C_(m,n)\cdot p^mq^(m-n)`

Where C is the combinatorial formula:

`C_(m,n)=(m!)/(n!\cdot(m-n)!)`

Substitute the given values in the formula:

`P=(17!)/(2!\cdot15!)\cdot0.43^2\cdot0.57^(15)`

Calculating:

`\begin{gathered} P=136\cdot0.1849\cdot0.0002178 \\ P=0.0055 \end{gathered}`

The probability is 0.0055 or 0.55%