Question

On average, four students visits the Mathematics and Statistics tutoring centre during a 5-minute period.  

(a) Calculate the probability that three students visit the center during a 5- minute period. 

(b) During a ten-minute period, what is the probability that at least 4 students visit the centre? 

Answer 1

Use Poison distribution

$a. \lambda=4$ k=3

$P(k)=\frac{\lambda^ke^{-\lambda}}{k!}$

$P(3)=\frac{4^3e^{-4}}{3!}=0.195$

b. $\lambda=8$

$P(X \ge4)=1-(P(0)+P(1)+P(2)+P(3))$

$P(0)=\frac{8^0e^{-8}}{0!}=0.0003$

$P(1)=\frac{8^1e^{-8}}{1!}=0.0027$

$P(2)=\frac{8^2e^{-8}}{2!}=0.0107$

$P(3)=\frac{8^3e^{-8}}{3!}=0.0286$

$P(X\ge4)=1-(0.0003+0.0027+0.0107+0.0286)=0.9577$