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The number of machine breakdowns in a month follows a Poisson distribution with a mean of 3. An insurance contract covers repairs to the machine if more than N breakdowns occur in a month. N is selected to be the highest number such that the contract will provide repairs in at least 25% of the months. Determine N.

Respuesta :

Answer:

N= 3

Step-by-step explanation:

given data

mean [tex]\lambda[/tex] =  3

provide repairs at least =  25%

solution

as here for poisson distribution

P(X=k) = [tex]\frac{(\lambda )^ke^{-\lambda }}{k!}[/tex]   ......................1

so here

P(X>n) = 0.25

and

P(X>n) = [tex]e^{-3 } \sum_{X=n}^{\infty } \frac{(3 )^k}{k!}\geq 0.25[/tex]      ..............2

so

P(X>3) = 0.3528

and

P(X>4) = 0.1847

so here  

N= 3

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