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?

The probability that no flaws occur in a certain portion of wire of length 5 millimeters is 0.055%

Poisson distribution is used when there are several occurrences in a distribution. It is given by:

For a 5 mm wire:

E(X) = 5mm * 1.5 flaws per mm = 7.5 mm

P(X = 0) =

The probability that no flaws occur in a certain portion of wire of length 5 millimeters is 0.055%

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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

Step 2:-

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

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

24 units

step-by-step explanation: