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Sagot :
Answer:
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.
Step-by-step explanation:
Mean for a number of units, which means that the Poisson distribution is used to solve this question.
Poisson Distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean:
3 defective for 1000, how many for 50?
3 - 1000
[tex]\mu[/tex] - 50
Applying cross multiplication:
[tex]\mu = \frac{3*50}{1000} = 0.15[/tex]
What is the probability that an order of 50 units will have one or more faulty units?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.15}*(0.15)^{0}}{(0)!} = 0.8607[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8607 = 0.1393[/tex]
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.
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