Question

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with a average of 5 phone calls during IO-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

The correct option is D $\frac{6}{e^5}$

According to Poisson distribution
$P(X=r)=\frac{e^{-m}{m}^r}{r!}$
$\therefore P(X\le 1)=P(X=0)+P(X=1)$
$=e^{-m}+\frac{e^{-m}m}{1!}$
Given m $=$mean$=5$
$\therefore P(x\le 1)=e^{-5}+5\times e^{-5}=e^{-5}(1+5)=\frac{6}{e^5}$