The number of calls coming into a hotels reservation center

The number of calls coming into a hotel\'s reservation center averages three per minute, a Find the probability that no calls will arrive in a given 1-minute period, Find the probability that at least two calls will arrive in a given 1-minute period, Find the probability that at least two calls will arrive in a given 2-minute period.

Solution

a. X~Poisson(=3 per minute)

P(X=x)=(3^x)*(exp(-3))/x!

So P(X=0)=(3^0)*(exp(-3))/1=0.04978707

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b. P(X>=2)=1-P(X=0)-P(X=1)

=1-(3^0)*(exp(-3))/1 - (3^1)*(exp(-3))/1

= 0.8008517

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c. X~Poisson(=6 in 2 minutes)

P(X=x)=(6^x)*(exp(-6))/x!

So P(X>=2)=1-P(X=0)-P(X=1)

=1-(6^0)*(exp(-6))/1 -(6^1)*(exp(-6))/1

=0.9826487