Question

My friend stella used to work in a taxi call centre . On any normal day she would expect to take 6calls every 10minutes.

1. What is the probability that she takes 6calls in the next 10 minutes
2. she takes a short break between 1023 and 1028 what is the probability that she misses no calls in this period.

Answer 1

Solution:

Given, $\lambda=6\ calls/10\ min=0.6\ calls/ min$

$X\sim Poi(\lambda)$

(1):

$P(X=6)=e^{-6}\times\dfrac{6^6}{6!}=0.1606$

(2):

Between 10:23 and 10:28, the time duration is 5 minutes.

So, $\lambda=3\ calls/5\ min$

$P(X=0)=e^{-3}\times\dfrac{3^0}{0!}=0.04978$

Now, required probability$=1-0.04978=0.95022$