Question

7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?

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Birdie

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To solve this problem, we can use the Poisson distribution, which is commonly used to model the number of events that occur in a fixed interval of time or space.

The Poisson distribution is defined by the parameter λ, which represents the average number of events in the given interval.

In this case, the average number of errors in 150-page prints is 6. So, the parameter λ is given by:

λ = Average number of errors per page * Number of pages

λ = (6 errors / 150 pages) * 1200 pages

λ = 48

Now, we can use the Poisson distribution formula to calculate the probability of having 48 errors in a 1200-page job:

P(X = x) = (e^(-λ) * λ^x) / x!

where P(X = x) is the probability of having x errors, e is the base of the natural logarithm, and x! represents the factorial of x.

Plugging in the values, we have:

P(X = 48) = (e^(-48) * 48^48) / 48! = 0.0575

The Poisson distribution is defined by the parameter λ, which represents the average number of events in the given interval.

In this case, the average number of errors in 150-page prints is 6. So, the parameter λ is given by:

λ = Average number of errors per page * Number of pages

λ = (6 errors / 150 pages) * 1200 pages

λ = 48

Now, we can use the Poisson distribution formula to calculate the probability of having 48 errors in a 1200-page job:

P(X = x) = (e^(-λ) * λ^x) / x!

where P(X = x) is the probability of having x errors, e is the base of the natural logarithm, and x! represents the factorial of x.

Plugging in the values, we have:

P(X = 48) = (e^(-48) * 48^48) / 48! = 0.0575

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