Answer:
0.1091 or 10.91%
Step-by-step explanation:
We have been given that a particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls involve fax messages and consider a sample of 20 calls. We are asked to find the probability that exactly 6 of the calls involve a fax message.
We will use Bernoulli's trials to solve our given problem.
[tex]P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}[/tex]
[tex]P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}[/tex]
[tex]P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}[/tex]
[tex]P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)[/tex]
[tex]P(X=6)=38760\cdot (0.000064)(0.04398046511104)[/tex]
[tex]P(X=6)=0.1090997009730[/tex]
[tex]P(X=6)\approx 0.1091\\[/tex]
Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.
