The time (in minutes) between arrivals of customers to a post office is to be mo

Question

The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.74. Please give your answers to two decimal places.

Part a)
the probability that the time between consecutive customers is less than 15 seconds?
0.286689

Part b)
the probability that the time between consecutive customers is between ten and fifteen seconds.
0.085025

Part c) need a solution
Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?

Explanation / Answer

C)

Here, 0.74 min = 44.4 s.

Note that

P(x>15|x>10) = P(X>15)/P(x>10)

Hence, as P(x>c) = exp(-x/u), where u = 44.4 s, then

P(x>15|x>10) = P(X>15)/P(x>10)

= exp(-15/44.4)/exp(-10/44.4)

= 0.893496722 [ANSWER]

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