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The time it takes a printer to print a job is an Exponential random variable with the expectation of 15 seconds. You send a job to the printer at 4:00 pm, and it appears to be forth in line. What is the probability that your job will be ready before 4:01 pm

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Answer:

0.56652

Step-by-step explanation:

Given that :

1 job takes 15 seconds

x jobs will take 60 seconds

15x = 60

x = 4

4 jobs take 60 seconds

μ = 4

Job is 4th in line :

Find the probability of ;

P(x ≥ 4) = 1 - [P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)]

P(μ, x) = [(e^-μ) * (μ^x)] ÷ x!

Using the poisson distribution calculator :

P(x< 3) = 0.19537

P(x< 2) = 0.14653

P(x< 1) = 0.07326

P(x< 0) = 0.01832

Hence,

P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)

= 1 - (0.19537 + 0.14653 + 0.07326 + 0.01832)

= 1 - 0.43348

= 0.56652

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