How Does Poisson Distribution Estimate Flaws in a 40 Square Foot Metal Sheet?

In summary, the probability of there being 3 or more flaws in a 8 x 5 feet area with a rate of 1 flaw per 10 square feet can be calculated using the Poisson distribution formula e^-np * np^k/k!. To find the value of np, we can consider the equivalent of 1 flaw per 10 x 10 feet as 0.1 flaw per 1 x 1 feet, which would be the same as 1 flaw per 100 square feet. Therefore, in an 8 x 5 feet area, we can expect 0.4 flaws. This means that the probability of there being 3 or more flaws is very low. It may seem like a difficult problem
  • #1
semidevil
157
2
so flaws in metal produced by high temperatures occur at a rate of 1 per 10 square feet. what is the probability that there is 3 or more flaws in a 8 x 5 feet.

ok, so I know we need to use poisson disstribution on this, e^-np * np^k/k!.

howver, I don't know my np.

so 1 per 10 square feet means 1 per 10 x 10 feet...maybe we can say this is the same as .1 per 1 x 1 feet.

so how do I put this in terms of 8 x 5 feet?
 
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  • #2
8*5 = 40 square feet...
you have 1 per 10 square feet... that's means...

even a 10 years old kids can do this problem...

what grade are you in? I don't realize middle school teachers start teaching poisson equation to the 7th grader...
 
  • #3
vincentchan said:
8*5 = 40 square feet...
you have 1 per 10 square feet... that's means...

even a 10 years old kids can do this problem...

what grade are you in? I don't realize middle school teachers start teaching poisson equation to the 7th grader...


haha...whoops, wasn't thinking about this...I got it...haha
 

FAQ: How Does Poisson Distribution Estimate Flaws in a 40 Square Foot Metal Sheet?

What is a Poisson distribution problem?

A Poisson distribution problem is a statistical problem that involves analyzing the probability of a certain number of events occurring within a given time or space. It is often used to model rare events or phenomena that occur randomly and independently of each other.

What are the characteristics of a Poisson distribution?

A Poisson distribution is characterized by two parameters: the mean number of events (λ) and the time or space interval (t) in which the events are observed. It is also a discrete probability distribution, meaning that the possible outcomes are whole numbers and the probabilities of each outcome are independent of each other.

How is a Poisson distribution different from a normal distribution?

A Poisson distribution differs from a normal distribution in several ways. Firstly, a Poisson distribution deals with discrete outcomes while a normal distribution deals with continuous outcomes. Additionally, a Poisson distribution has only one parameter (λ) while a normal distribution has two (mean and standard deviation). Lastly, a Poisson distribution is used to model rare events while a normal distribution is used to model more common events.

What are some real-life applications of Poisson distribution?

Poisson distribution is commonly used in various fields such as finance, engineering, and biology. Some real-life applications include predicting the number of customers arriving at a store, the number of accidents occurring on a highway, and the number of phone calls received by a call center in a given time period.

How do you solve a Poisson distribution problem?

To solve a Poisson distribution problem, you need to know the value of λ (mean) and the time or space interval (t). Then, you can use the Poisson probability formula to calculate the probability of a specific number of events occurring within that time or space interval. Alternatively, you can use statistical software or a Poisson distribution table to find the probabilities.

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