Answer to Question #88251 in Statistics and Probability for lebogang

Question

4.2 At a major retail store, 25 percent of the employees use internet banking. For a randomly selected group of five employees, calculate the probability that three use internet banking

Answer 1

1.The number of observations or trials is fixed.

2.Each observation or trial is independent.

3.The probability of success  is exactly the same from one trial to another.

The number of users of internet banking follows Binomial distribution b(x; n, p)

$$P(X=x)=\begin{pmatrix} n \\ x \end{pmatrix}p^x(1-p)^{n-x}$$

We have that $n=5, p=0.25.$ Then the probability that three use internet banking is

$$P(X=3)=\begin{pmatrix} 5 \\ 3 \end{pmatrix}0.25^3(1-0.25)^{5-3}=0.087890625$$