The probability that at least 40 jobs will be submitted in 15 minutes is 0.79162.
The number of jobs submitted per minute follows Poisson Distribution.
A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X= x) = e^{-\lambda} \frac{\lambda^{x} }{x!}[/tex] .
In the question, we have the random variable x = 40.
The mean λ = Average jobs per minute*time = 3*15 = 45.
We are to find the probability that at least 40 jobs will be submitted in 15 minutes, which is represented as P(X ≥ 40) = P(X > 39).
P(X > 39) = 1 - P(X ≤ 39) = 1 - poissoncdf(45,39)
As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).
Therefore, P(X > 39) = 1 - 0.20838 = 0.79162.
Therefore, the probability that at least 40 jobs will be submitted in 15 minutes is 0.79162.
Learn more about the Poisson Distribution at
brainly.com/question/7879375
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