At a telephone enquiry system the number of phone cells regarding relevant enquiry follow …

Question

At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $5$ phone calls during $10$ minute time intervals. The probability that there is at the most one phone call during a $10$-minute time period is :

Accepted Answer

Required probability

$= P(X = 0) + P(X = 1)$

$$ = {{{e^{ - 5}}} \over {0!}}{5^0} + {{{e^{ - 5}}} \over {1!}}{5^1}$$

$= {e^{ - 5}} + 5{e^{ - 5}}$

$$ = {6 \over {{e^5}}}$$

Solutions · 1