Answer: 0.1353
Step-by-step explanation:
Given : The mean of failures = 0.025 per hour.
Then for 8 hours , the mean of failures = [tex]\lambda=8\times0.25=2[/tex] per eight hours.
Let X be the number of failures.
The formula to calculate the Poisson distribution is given by :_
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]
Now, the probability that the instrument does not fail in an 8-hour shift :-
[tex]P(X=0)=\dfrac{e^{-2}2^0}{0!}=0.1353352\approx0.1353[/tex]
Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353
