Question

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 samp what is the probability that exactly 6 of the calls involve a fax message?

Answer 1

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.

$P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}$

$P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}$

$P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}$

$P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)$

$P(X=6)=38760\cdot (0.000064)(0.04398046511104)$

$P(X=6)=0.1090997009730$

$P(X=6)\approx 0.1091$

Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.