Answer to Question #316016 in Statistics and Probability for EDWIN

Question

a)     A supermarket has two girls ringing up sales at the counters. If the service time for each customer is exponential with mean 4 minutes and if the people arrive in Poisson fashion at the rate of 10 per hour

a)        What is the probability of having to wait for service?                       

 b)       What is the expected percentage of idle time for each girl?              

 c) If a customer has to wait, what is the expected length of his waiting time?

Answer 1

a)

$P(n≥2)=\frac{1}{2!}(\frac{4}{6})^2*\frac{2(1/4)}{2(1/4)-(1/6)}*(1/2)=\frac{1}{6}$

b)

$1-(1/3)=2/3=67$ %

c)

$W_s=(4/6)^2*\frac{1/4}{[(1/2)-(1/6)^2]}*1/2 +4=4.5$ minutes