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By some miracle, a Smudgy Press book is found to have 90% of its pages free of typographic errors. Assuming that the distribution of the typographical errors per page is Poisson, what is the probability that a randomly selected page contains exactly one error

1 Answer

3 votes

Answer:

The value is
P(X = 1 ) = 0.0948

Explanation:

From the question we are told that

The the probability that the Smudgy Press book pages have zero errors
p = 0.90

Gnerally the probability distribution for Poisson distribution is


P(X = x) = (\lambda ^x * e^(-\lambda))/(x!)

Gnerally the probability that the Smudgy Press book pages have zero errors is mathematically represented as


P(X = 0) = (\lambda ^0 * e^(-\lambda))/(0!) =p= 0.90

=>
e^(-\lambda) =p= 0.90

taking natural log of both sides


ln (e^(-\lambda)) = ln(0.90)

=>
-\lambda = -0.1054

=>
\lambda = 0.1054

Generally the probability that a randomly selected page contains exactly one error is mathematically represented as


P(X = 1 ) = (\lambda ^1 * e^(-\lambda))/(1!)

=>
P(X = 1 ) = (0.1054 ^1 * e^(-0.1054 ))/(1!)

=>
P(X = 1 ) = 0.0948

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