A company produces optical fiber cable, then the answer to four decimal place is P ( x < 3 ) = 0.089.
Based on the given conditions,
A company produces optical fiber cable with a mean = 0.5 flaws
A company produces optical fiber cable with a mean = 100 feet
There will be less than 3 flaws and 1200 feet of cable
So,
We can write,
Mean = 0.5/100
Flaws f = 3
Distance [tex]d_{2}[/tex] = 1200feet
To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products.
Generally the equation for Poisson mean lambda over 1200 is mathematically given by,
λ = 0.5 * [tex]\frac{1200}{100}[/tex]
λ = 0.5*12
λ = 6
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
P ( X = x ) = (e^-λ * λ^x )/ x!
Where,
x is the number of successes
e = 2.71828 is the Euler number
λ = is the mean in the given interval.
Hence,
P ( x < 3 ) = (e^-λ * λ^x )/ x!
P ( x < 3 ) = [tex]\frac{e^{-6}*6^{3} }{3!}[/tex]
P ( x < 3 ) = (0.00248 * 216)/3*2*1
P ( x < 3 ) = (0.00248 * 216)/6
P ( x < 3 ) = (0.5356)/6
P ( x < 3 ) = 0.089
Therefore,
A company produces optical fiber cable, then the answer to four decimal place is P ( x < 3 ) = 0.089.
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