Customer inter-arrival time follows exponential distribution. The average inter-

Question

Customer inter-arrival time follows exponential distribution. The average inter-arrival time is 5 minutes. What is the probability that the next customer will arrive in 3 minutes?

Question 3 options:

a)

0.1006

b)

0.4512

c)

0.0129

d)

None of the answers

e)

0.5488

customer inter-arrival time follows exponential distribution. The average inter-arrival time is 5 minutes. What is the probability that the next customer will arrive in 3 minutes?

a)

0.1006

b)

0.4512

c)

0.0129

d)

None of the answers

e)

0.5488

Explanation / Answer

Lambda = 1/5 = 0.2 customers per minute; x = 3 minutes

If the question means that the next arrival should be in 3 minutes or less, then the answer is computed using the cumulative distribution function.

F(x) = 1 - e[-Lambda*x]

Probability = 1 - EXP(-0.2*3) = 0.4512

But if it means exactly 3 minutes, then the answer is computed using the density function.

P(x) = Lambda*e[-Lambda*x]

Probability = 0.2*EXP(-0.2*3) = 0.1098

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