Respuesta :
Answer:
The probability of 4 or fewer unsuccessful plates in one hour is 0.00752.
Step-by-step explanation:
Let X = number of plates that are unsuccessful.
The expected number of unsuccessful plates per hour is, λ = 12.
The random variable X follows a Poisson distribution with parameter λ = 12.
The probability function of a Poisson distribution is:
[tex]P(X=X)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, ...[/tex]
Compute the probability of 4 or fewer unsuccessful plates in one hour as follows:
P (X ≤ 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)
[tex]=\frac{e^{-12}12^{0}}{0!}+\frac{e^{-12}12^{1}}{1!}+\frac{e^{-12}12^{2}}{2!}+\frac{e^{-12}12^{3}}{3!}+\frac{e^{-12}12^{4}}{4!}\\=0.0000+0.0000+0.00044+0.00177+0.00531\\=0.00752[/tex]
Thus, the probability of 4 or fewer unsuccessful plates in one hour is 0.00752.
