Answer:
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
3 failures every twenty weeks
This means that for 1 week, ![\mu = \frac{3}{20} = 0.15](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cfrac%7B3%7D%7B20%7D%20%3D%200.15)
Calculate the probability that there will not be more than one failure during a particular week.
Probability of at most one failure, so:
![P(X \leq 1) = P(X = 0) + P(X = 1)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%201%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29)
Then
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-0.15%7D%2A0.15%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.8607)
![P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-0.15%7D%2A0.15%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.1291)
Then
![P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898](https://tex.z-dn.net/?f=P%28X%20%5Cleq%201%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%3D%200.8607%20%2B%200.1291%20%3D%200.9898)
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
Three million five hundred thousand or three and a half million
Answer:
none
Step-by-step explanation:
becàuse it has thesame masses
Y = kx ⇒ k = y/x = 2/(-3) = -2/3
Answer: k = -2/3
Answer:
idk
Step-by-step explanation:
you need to add a picture