The number of defective circuit boards coming off a

Chapter 4, Problem 53E

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QUESTION:

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found.

a Find the probability that it was produced during the first hour of operation during that day.

b Find the probability that it was produced during the last hour of operation during that day.

c Given that no defective circuit boards were produced during the first four hours of operation, find the probability that the defective board was manufactured during the fifth hour.

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QUESTION:

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found.

a Find the probability that it was produced during the first hour of operation during that day.

b Find the probability that it was produced during the last hour of operation during that day.

c Given that no defective circuit boards were produced during the first four hours of operation, find the probability that the defective board was manufactured during the fifth hour.

ANSWER:

Step 1 of 3

One defective circuit board was found on the specific 8 hour day

a)

The claim is to find the probability that it was produced the first hour of operation during that day

Let X follows the uniform distribution with the limits 0 and 8

\(\begin{aligned}
\text { then, } f(x) & =\frac{1}{b-a} \\
P(0<X<1) & =\int_{0}^{1} \frac{1}{8-0} \mathrm{dx} \\
& =\frac{1}{8} \int_{0}^{1} \mathrm{dx} \\
& =\frac{1}{8}[\mathrm{x}]_{0}^{1} \\
& =\frac{1}{8}
\end{aligned}\)

Hence, the probability that it was produced the first hour of operation during that day is \(\frac{1}{8}\)

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