Question

Assume that when adults with smartphones are randomly selected , 52% use them in meetings or classes. If 7 adults smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.The probability is:

Answer 1

From the information available;

The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;

`\begin{gathered} p=52\text{ \%, OR 0.52} \\ n=7 \\ p(X=x) \\ We\text{ shall now apply;} \\ p(X=4)=(n!)/(x!(n-x)!)* p^x*(1-p)^(n-x) \end{gathered}`

We shall insert the values as follows;

`\begin{gathered} p(X=4)=(7!)/(4!(7-4)!)*0.52^4*(1-0.52)^(7-4) \\ =(5040)/(24(6))*0.07311616*0.110592 \\ =35*0.07311616*0.110592 \\ =0.28301218 \end{gathered}`

Rounded to four decimal places, this becomes;

`(\text{selecting exactly 4)}=0.2830`

ANSWER:

The probability of selecting exactly 4 smartphone users is 0.2830