Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
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.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
