Question
In: Statistics and Probability
Assume that customer arrivals at a barber shop are random and independent of one another, and...
Assume that customer arrivals at a barber shop are random and independent of one another, and the number of customer arrivals at a barber shop and the time until the next customer arrives is independent.
(a) In city A, on average, 3 customers arrive at a barber shop every hour. Using an appropriate probability distribution,
(i) find the probability that at least 5 customers arrive at a barber shop every hour.
(ii) A sample of 25 barber shops in city A was obtained. Find the probability that at least 3 barber shops were visited by at least 5 customers.
(iii) A customer has just arrived in a barber shop. Find the probability that the time, until the next customer arrives will be at most 2 hours (from now).
Solutions
orchestra answered 1 year agoRelated Solutions
Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and...
Campus Barber Shop has one barber. Customers arrive at a rate of
2.2 per hour, and haircuts are given at a rate of 3 per hour.
Assume the basic Poisson-Exponential model and answer the following
questions.
What is the probability that the barber is idle?
What is the probability that one customer is getting a haircut
and no one is waiting in the line?
What is the probability that one customer is receiving a haircut
and one customer is in...
It takes a barber 15 minutes to serve one customer. a. What is...
It takes a barber 15 minutes to serve one customer.
a.
What is the capacity of the barber expressed in customers per hour?
customers per hour
b.
Assuming the demand for the barber is 2 customers per hour, what is the flow rate?
customers per hour
c.
Assuming the demand for the barber is 2 customers per hour, what is the utilization?
percent
...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9 (Algorithmic)
Marty's Barber Shop has one barber. Customers have an arrival
rate of 2.1 customers per hour, and haircuts are given with a
service rate of 5 per hour. Use the Poisson arrivals and
exponential service times model to answer the following
questions:
What is the probability that no units are in the system? If
required, round your answer to four decimal places.
P0 =
What is the probability that one customer is receiving a
haircut and no...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9
(Algorithmic)
Marty's Barber Shop
has one barber. Customers have an arrival rate of 2.1 customers per
hour, and haircuts are given with a service rate of 4 per hour. Use
the Poisson arrivals and exponential service times model to answer
the following questions:
What is the probability that no units are in the system? If
required, round your answer to four decimal places.
P0 = ?????
What is the probability that one customer is receiving a
haircut and...
Assume a standard customer, Johnny Rose, at a shop will spend 20 mins in the shop....
Assume a standard customer, Johnny Rose, at a shop will spend 20
mins in the shop. The shop has 4 customers on average and service
time is random with known distribution. The shop has 4 customers on
average and service time is random with known distribution. How
many customers does the shop serve during a typical open hour?
Now let's say the shop would like to decrease the average number
of customers at any point, but assume it cannot control/influence...
Consider product A and product B who have independent demands from one another. Now assume that...
Consider product A and product B who have independent demands
from one another. Now assume that both demands are normally
distributed with same cost structure. Using the newsvendor model
(how to make inventory decisions under uncertainty of demand) - if
the demand is combined or pooled for products A and B, will the
TOTAL inventory increase or decrease vs. making separate decisions
for the two products? Show work and arguments very carefully. (25
marks / 100)
Please help - this...
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?
Assume that X, Y, and Z are independent random variables and that each of the random...
Assume that X, Y, and Z are independent random variables and
that each of the random variables have a mean of 1. Further, assume
σX = 1, σY = 2, and σZ = 3. Find
the mean and standard deviation of the following random
variables:
a. U = X + Y + Z
b. R = (X + Y + Z)/3
c. T = 2·X + 5·Y
d. What is the correlation between X and Y?
e. What is the...
produce the pseudo code for the Barber routine Clipaway() and the Customer routine Cutmyhair() such that...
produce the pseudo code for the Barber routine Clipaway() and
the Customer routine Cutmyhair() such that each customer is given a
customized haircut and each customer pays for the Barber’s
service.
The Sleeping Barber Problem This works for a shop that holds a
total of N customers with one barber. If a customer cannot enter
the shop, the customer will be forced into the street. Start the
Barber before the customers.
Shared variables:
const int num_chairs = N; // number...
2. Assume that X1, . . . , Xn are independent copies of the random variable...
2. Assume that X1, . . . , Xn are independent copies of the
random variable X = Y + V , where Y ∼ N(µ, σ2 ) and V ∼
U(−ν, ν), ν > 0, and Y and V are independent. We will consider
the hypotheses
H0 : µ = µ0 and
HA : µ does not equal µ0.
(a) It can be shown that E(X) = µ and var(X) = σ2 +
ν2/3. Set µ = 60, σ...
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