Answer:
The probability that the instrument does not fail in an 8-hour shift is ![P(X=0) \approx 0.8659](https://tex.z-dn.net/?f=P%28X%3D0%29%20%5Capprox%200.8659)
The probability of at least 1 failure in a 24-hour day is ![P(X\geq 1 )\approx 0.3508](https://tex.z-dn.net/?f=P%28X%5Cgeq%201%20%29%5Capprox%200.3508)
Step-by-step explanation:
The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:
![P(X)=\frac{e^{-\mu}\mu^x}{x!}](https://tex.z-dn.net/?f=P%28X%29%3D%5Cfrac%7Be%5E%7B-%5Cmu%7D%5Cmu%5Ex%7D%7Bx%21%7D)
Let X be the number of failures of a testing instrument.
We know that the mean
failures per hour.
(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:
For an 8-hour shift, the mean is ![\mu=8\cdot 0.018=0.144](https://tex.z-dn.net/?f=%5Cmu%3D8%5Ccdot%200.018%3D0.144)
![P(X=0)=\frac{e^{-0.144}0.144^0}{0!}\\\\P(X=0) \approx 0.8659](https://tex.z-dn.net/?f=P%28X%3D0%29%3D%5Cfrac%7Be%5E%7B-0.144%7D0.144%5E0%7D%7B0%21%7D%5C%5C%5C%5CP%28X%3D0%29%20%5Capprox%200.8659)
(b) To find the probability of at least 1 failure in a 24-hour day, you need to:
For a 24-hour day, the mean is ![\mu=24\cdot 0.018=0.432](https://tex.z-dn.net/?f=%5Cmu%3D24%5Ccdot%200.018%3D0.432)
![P(X\geq 1 )=1-P(X=0)\\\\P(X\geq 1 )=1-\frac{e^{-0.432}0.432^0}{0!}\\\\P(X\geq 1 )\approx 0.3508](https://tex.z-dn.net/?f=P%28X%5Cgeq%201%20%29%3D1-P%28X%3D0%29%5C%5C%5C%5CP%28X%5Cgeq%201%20%29%3D1-%5Cfrac%7Be%5E%7B-0.432%7D0.432%5E0%7D%7B0%21%7D%5C%5C%5C%5CP%28X%5Cgeq%201%20%29%5Capprox%200.3508)
The answer is 19......................................................................................................................................................................................................................
Answer:
b8
Step-by-step explanation:
Answer:
$45
Step-by-step explanation:
One ticket costs $9
They bought 5 tickets
9*5=45