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The number of calls coming into a hotel’s reservation during any fixed timeinterval will follow a...

The number of calls coming into a hotel’s reservation during any fixed timeinterval will follow a Poisson distribution. Previous experience show that onaverage, three calls will come into this reservation center per minute.

(a) (2 points) Calculate the probability that no calls will arrive in a random1-minute period.

(b) (4 points) Calculate the probability that at least two calls will arrivein a random 1-minute period.

(c) (4 points) Calculate the probability that at least two calls will arrivein a random 2-minute period.

(d) (4 points) Calculate the expected value of the number of calls thatarrive in a random 3-minute period.

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