Answer:
The probability that there are 8 occurrences in ten minutes is
option B. 0 .0771
Step-by-step explanation:
Given:
Random Variable = x
Mean number of occurrences in ten minutes is 5.3.
The probability of an occurrence is the same in any two time periods of an equal length
To Find:
The probability that there are 8 occurrences in ten minutes = ?
Solution:
Let X be the number of occurrences of the event X
![X \sim {Pois} (\lambda)](https://tex.z-dn.net/?f=X%20%5Csim%20%7BPois%7D%20%28%5Clambda%29)
![\lambda = E(X) = 5.3](https://tex.z-dn.net/?f=%5Clambda%20%3D%20E%28X%29%20%3D%205.3)
Possion of distribution is given by ,
![P(X=x) = \frac{e^{- \lambda} \lambda^{x}}{x!}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cfrac%7Be%5E%7B-%20%5Clambda%7D%20%5Clambda%5E%7Bx%7D%7D%7Bx%21%7D)
Substituting the values,
![P(X=8) = \frac{e^{- 5.3} 5.3^{8}}{8!}](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%20%5Cfrac%7Be%5E%7B-%205.3%7D%205.3%5E%7B8%7D%7D%7B8%21%7D)
![P(X=8) = \frac{(0.004994) ( 622596.904)}{40320}](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%20%5Cfrac%7B%280.004994%29%20%28%20622596.904%29%7D%7B40320%7D)
![P(X=8) = \frac{(3109.24894)}{40320}](https://tex.z-dn.net/?f=P%28X%3D8%29%20%3D%20%5Cfrac%7B%283109.24894%29%7D%7B40320%7D)
P(X=8) = 0.0771
The awnser to this question is 200 and 300
I think it’s the third one
Answer:
Andre's
Step-by-step explanation
I think its Andre. I apologize if it is not.