Question

Consider the case of a grocery store where the interarrival time between two customers
consecutively entering the store is known to be exponentially distributed. Previously
collected data shows that 1800 customers were recorded to have entered the store in
300 hours. Answer the following:
(a) What is the probability density function for the inter-arrival time (in minutes)
between two consecutively arriving customers? (15)

(b) What is the probability that the next customer will arrive AFTER five minutes? (10)

(c) What is the mean and standard deviation of the inter-arrival times? (5+5=10)

Answer 1

here inter arrival time will follows exponential distribution with parameter

β =300*60/1800 =10 minute/customer

a)

f(x)=(1/β)e-x/β=

(1/10)e-x/10 for x>=0

b)

P(X>5)=1-P(X<5)=1- f(x) dx =1- (1/10)e-x/10 dx =1-(1-e(-5/10))=

0.6065

c)for exponential distribution:

mean μ =

β =

10.00

standard deviation σ=

=β =

10.00