Question

You are trying to electroplate a new superconducting ceramic-metal onto a circuit board. The rate at which a plating will be unsuccessful is about 12 per hour. You implement a new deposition process. What is the probability that you find 4 or fewer unsuccessful plates in one hour?

Answer 1

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:

$P(X=X)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, ...$

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)

              $=\frac{e^{-12}12^{0}}{0!}+\frac{e^{-12}12^{1}}{1!}+\frac{e^{-12}12^{2}}{2!}+\frac{e^{-12}12^{3}}{3!}+\frac{e^{-12}12^{4}}{4!}\\=0.0000+0.0000+0.00044+0.00177+0.00531\\=0.00752$

Thus, the probability of 4 or fewer unsuccessful plates in one hour is 0.00752.