Question

For a certain type of copper wire, it is knownthat, on the average, 1.5 flaws occur per millimeter.Assuming that the number of flaws is a Poisson randomvariable, what is the probability that no flaws occur ina certain portion of wire of length 5 millimeters?

Answer 1

Answer:

The probability that no flaws occur in a certain portion of wire of length 5 millimeters =  1.1156 occur / millimeters

Step-by-step explanation:

Step 1:-

Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.

by  Poisson random variable given that λ = 1.5 flaws/millimeter

Poisson distribution $P(X= r) = \frac{e^{-\alpha } \alpha ^{r} }{r!}$

Step 2:-

The probability that no flaws occur in a certain portion of wire

$P(X= 0) = \frac{e^{-1.5 } \(1.5) ^{0} }{0!}$

On simplification we get

P(x=0) = 0.223 flaws occur / millimeters

Conclusion:-

The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters