Answer:
The required probability is 0.167
Step-by-step explanation:
Consider the provided information.
Let x be the number of breakdown per day.
A new automated production process averages 1.4 breakdowns per day.
λ=1.4
Probability of having three or more breakdowns during a day is:
[tex]P(x\geq 3)=1-[f(0)+f(1)+f(2)][/tex]
The Poisson probability function is: [tex]f(x)=\frac{\lambda^xe^{-\lambda}}{x!}[/tex]
Therefore the required probability is:
[tex]P(x\geq 3)=1-[\frac{\left(1.4^{0}e^{-1.4}\right)}{0!}+\frac{\left(1.4^{1}e^{-1.4}\right)}{1!}+\frac{\left(1.4^{2}e^{-1.4}\right)}{2!}][/tex]
[tex]P(x\geq 3)\approx1-0.833[/tex]
[tex]P(x\geq 3)=0.167[/tex]
Hence, the required probability is 0.167
