Answer:
250%
Step-by-step explanation:
(2 1/2) × 100%
= 250%
= 2.5
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}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5EnC_x%5Ccdot%20P%5Ex%281-P%29%5E%7Bn-x%7D)
![P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}](https://tex.z-dn.net/?f=P%28X%3D6%29%3D%5E%7B20%7DC_6%5Ccdot%20%280.20%29%5E6%281-0.20%29%5E%7B20-6%7D)
![P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}](https://tex.z-dn.net/?f=P%28X%3D6%29%3D%5Cfrac%7B20%21%7D%7B6%21%2820-6%29%21%7D%5Ccdot%20%280.20%29%5E6%280.80%29%5E%7B14%7D)
![P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)](https://tex.z-dn.net/?f=P%28X%3D6%29%3D%5Cfrac%7B20%21%7D%7B6%21%2814%29%21%7D%5Ccdot%20%280.000064%29%280.04398046511104%29)
![P(X=6)=38760\cdot (0.000064)(0.04398046511104)](https://tex.z-dn.net/?f=P%28X%3D6%29%3D38760%5Ccdot%20%280.000064%29%280.04398046511104%29)
![P(X=6)=0.1090997009730](https://tex.z-dn.net/?f=P%28X%3D6%29%3D0.1090997009730)
![P(X=6)\approx 0.1091\\](https://tex.z-dn.net/?f=P%28X%3D6%29%5Capprox%200.1091%5C%5C)
Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.