9- The Department of Motor Vehicles (DMV) can service customers at a rate of 30

Question

9- The Department of Motor Vehicles (DMV) can service customers at a rate of 30 per hour (or 1/2 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take more than 4 minutes for a particular customer to get a license renewal once they begin service?

10 - Arrivals at a fast-food restaurant follow a Poisson distribution with a mean of 8 customers in an hour. What is the probability that in the next hour there will be strictly less than 6 arrivals?

Explanation / Answer

9.)   = 2

P(x > 4) = 1 - P(x 4)

= 1 - [1 - exp(-4*2)] = e-8

10.) µ = 8; x < 6

P(x; ) = (e-) (x) / x!

  P(x < 6, 8) = P(0; 8) + P(1; 8) + P(2; 8) + P(3; 8) + P(4; 8) + P(5; 8)

= 0.1912

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