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t the Fidelity Credit Union, a mean of 5.8 customers arrive hourly at the drive-through window. What is the probability that, in any hour, more than 5 customers will arrive? Rot the Fidelity Credit Union, a mean of 5.8 customers arrive hourly at the drive-through window. What is the probability that, in any hour, more than 5 customers will arrive? Round your answer to four decimal places.und your answer to four decimal places.

Respuesta :

ajeigbeibraheem

Answer:

0.5217

Step-by-step explanation:

Given that:

mean [tex]\mu[/tex] = 5.8

Using Poisson Probability formula:

[tex]P(X=x) = \frac{ (e^{- \mu} * {\mu^x) }}{x!}[/tex]

[tex]P(X>5.8)=1-P(X \leq5)[/tex]

[tex]= 1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)][/tex]

[tex]= 1 -[\frac{(e^{-5.8}*5.8^0) }{ 0! } + \frac{(e^{-5.8}*5.8^1) }{ 1! } +\frac{(e^{-5.8}*5.8^2) }{ 2! } +\frac{(e^{-5.8}*5.8^3) }{ 3! } +\frac{(e^{-5.8}*5.8^4) }{ 4! } +\frac{(e^{-5.8}*5.8^5) }{ 5! } ][/tex]

[tex]=1-(0.003+0.0176+0.0509+0.0985+0.1428+0.1656)[/tex]

[tex]=1-0.4783[/tex]

[tex]=0.5217[/tex]

∴ the probability that, in any hour, more than 5 customers will arrive =0.5217