Use two different computations (one involving the Poisson and another the exponential random variable) to determine the probability that no job will arrive during the next 15 minutes.

Probability according to Poisson's distribution function = 0.04979

Probability according to Exponential random variable = 0.3333

Step-by-step explanation:

In 15 minutes, the number of jobs that arrive on the average = (12/60) * 15 = 3 jobs per 15 minutes

Poisson distribution formula is given as

P (X = x) = (e^-λ) (λˣ) / x!

λ = mean = 3 jobs per 15 minutes

x = variable whose probability is required = 0

P (X = 0) = (e⁻³) (3⁰) / 0! = 0.04979

Exponential random variable formula is given by

P (X=x) = f (x,λ) = λ e^ (-λ. x)

λ = rate parameter, that is, time between jobs.

λ = (1/3) (15 minutes per job) = 0.3333

P (X = 0) = f (0, 0.3333) = 0.3333 e^0 = 0.3333