The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.025 failures per hour. (a) What is the probability that the instrument does not fail in an 8-hour shift

Answer: 0.1353Step-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