Question
In: Statistics and Probability
Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two...
Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two every 6 minutes.
(a) Using the Poisson distribution calculate the probability of two or more customersarrive in a 2-minute period.
(b) Consider X denote number of customers and X follows binomial distribution withparametersn= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.
(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) Whatis the pdf ofY? (ii) Findq1=π0.75
(d) Let Y denote the waiting time in minutes until the first customer arrives. What isthe probability that the shopkeeper will have to wait more than 3 minutes for thearrival of the first customer ?
(e) What is the probability that shopkeeper will wait more than 3 minutes before bothof the first two customers arrive?
Solutions
orchestra answered 1 year agoRelated Solutions
Customers arrive in a certain shop according to an approximate Poisson process on the average of...
Customers arrive in a certain shop according to an approximate
Poisson process on the average of two every 6 minutes.
(a) Using the Poisson distribution calculate the probability of
two or more customers arrive in a 2-minute period.
(b) Consider X denote number of customers and X follows binomial
distribution with parameters n= 100. Using the binomial
distribution calculate the probability oftwo or more customers
arrive in a 2-minute period.
(c) Let Y denote the waiting time in minutes until...
Customers arrive at a department store according to a Poisson process with an average of 12...
Customers arrive at a department store according to a Poisson
process with an average of 12 per hour.
a. What is the probability that 3 customers arrive between
12:00pm and 12:15pm?
b. What is the probability that 3 customers arrive between
12:00pm and 12:15pm and 6 customers arrive between 12:30pm and
1:00pm?
c. What is the probability that 3 customers arrive between
12:00pm and 12:15pm or 6 customers arrive between 12:30pm and
1:00pm?
d. What is the probability that a...
Customers arrive at a hair salon according to a Poisson process with an average of 16...
Customers arrive at a hair salon according to a Poisson process
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close whenever the worker leaves. assume that customers who arrive
while the salon is closed leave immediately and don’t wait until
the worker returns. The salon is closed on weekends.
a.
What is the probability that at most (less than) four customers
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Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There...
Customers arrive at a cafe every 2 minutes on average according
to a Poisson process. There are 2 employees working at the bar
providing customer service, i.e., one handling customer orders and
another handling payments. It takes an average of 1 minute to
complete each order (exponentially distributed). Based on the
above:
f. What are the service time probability density and cumulative
distribution functions?
g. What percentage of customer orders will be prepared in
exactly 2 minutes?
h. What are...
Suppose we have a single server in a shop and customers arrive in the shop with...
Suppose we have a single server in a shop and customers arrive
in the shop with a Poisson arrival distribution at a mean rate of
λ=0.5 customers per minute. The interarrival time have an
exponential distribution with the average inter-arrival time being
2 minutes. The server has an exponential service time distribution
with a mean service rate of 4 customers per minute. Calculate: 1.
Overall system utilization 2. Number of customers in the system 3.
Number of customers in the...
A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
A queueing system serves two types of customers. Type 1
customers arrive according to a Poisson process with a mean rate of
5 per hour. Type 2 customers arrive according to a
Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
a. What is the probability distribution...
A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
A queueing system serves two types of customers. Type 1
customers arrive according to a Poisson process with a mean rate of
5 per hour. Type 2 customers arrive according to a
Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
a. What is the probability distribution...
A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
A queueing system serves two types of customers. Type 1
customers arrive according to a Poisson process with a mean rate of
5 per hour. Type 2 customers arrive according to a
Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
a. What is the probability distribution...
A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.
A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.
(a) Construct the distribution for the random variable X?
(b) Find the mean and standard deviation of X.
(c) What is the probability that the time between consecutive arrivals (customers) will fall between 3 and 6 minutes?
Customers arrive at a two-server system according to a Poisson process having rate λ = 5....
Customers arrive at a two-server system according to a Poisson
process having rate λ = 5. An arrival finding server 1 free will
begin service with that server. An arrival finding server 1 busy
and server 2 free will enter service with server 2. An arrival
finding both servers busy goes away. Once a customer is served by
either server, he departs the system. The service times at server i
are exponential with rates μi, where μ1 = 4, μ2...
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