Question

The number of calls arriving at a call center are received at a rate of 5 calls per minute. So:

I. The expected time that elapses between calls is 15 seconds.

II. The probability that between consecutive calls elapse at most 10 seconds is 0.4346.

a. Both are correct.

b. None is correct

c. Only I is correct

d. Only II is correct

Answer 1

Let X denote the time between two consecutive call (in minutes). Then $X\sim exp(\lambda=5)$

So, Expected time that lapses between calls = $E(X)=\frac{1}{\lambda}=\frac{1}{5}min=\frac{1}{5}\times 60 seconds=12seconds$

Also, $F(x)=P(X<x)=1-e^{-\lambda x}=1-e^{-5x},x>0$

Now, $P(X<10)=1-e^{-5(\frac{10}{60})}=0.5654$

So, none are correct.

Hence option B.