Question

At a telephone enquiry system the number of phone calls 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

• A. $\frac{6}{5^e}$
• B. $\frac{5}{6}$
• C. $\frac{6}{55}$
• D. $\frac{6}{e^5}$

Answer 1

Answer: (D)

$\frac{6}{e^5}$

Answer 2

$P\left(X =r\right) = \frac{e^{-m}m^{r}}{r!}$ P (at most 1 phone call) $= P\left(X \le 1\right) = P\left(X = 0\right) + P\left(X = 1\right)$ $= e^{-5} + 5 \times e^{-5} = \frac{6}{e^{5}}$