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%

Find out more at: link

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

42.4

step-by-step explanation:

convert to decimal

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.