Question

Individual customers arrive at a coffee shop after it opens at 6 AM. The number of customers arriving by 7AM has a Poisson distribution with parameter λ = 10. 25% of the customers buy a single donut and coffee, and 75% just buy coffee. Each customer acts independently. Answer the following:

a.What are the two random variables described above and what are their probability

mass functions?

b.What is the probability that exactly five customers arrive by 7AM?

c.If 10 customers enter by 7AM, what is the probability that five donuts are

purchased?

d.What is the expected number (true mean) of donuts a single customer will

purchase, and what is the expected number of customers that arrive by 10AM?

Answer #1

**Part a.**

The 2 random variables are,

X : the number of customers arriving by 7 AM.

Z : No. of donuts bought by X customers.

&

**Part
b.**

**Part
c.**

Let Z be the random variable denoting the number of donuts bought.

Then ,

To compute,

**Part d.**

expected number (true mean) of donuts a single customer will purchase is,

what is the expected number of customers that arrive by 10AM is,

************************************************* HENCE THE ANSWER *******************************************

At ABC Bank, customers arrive at a teller line at a rate of 10
per five-minute period. Assuming that customers arrive randomly and
independently, use the Poisson probability distribution to answer
the following questions: (8 points)
a.What is the probability that no customers arrive in a
five-minute period?
b.What is the probability that 3 or fewer customers arrive in a
five-minute period?
c.What is the probability that no customers arrive in a
one-minute period?
d.What is the probability that at...

Customers arrive at a common queue at the coffee station with
two identical coffee machines in a busy mall at the rate of 48 per
hour, following Poisson distribution. Each customer mixes his or
her specialty coffee taking 2 minutes on an average following an
exponential process. What is the expected number of customers in
the system at this coffee station?
please show work!

Let ? be the number of female customers who arrive at a barber
shop before the first male customer arrives. The probability of a
female customer arriving at the barber shop is 0.75.
(i) Find ?(? ≥ 8).
(ii) In a random sample of size 36, find the normal
approximation for ?(2.5 ≤ ?̅ ≤ 3.5), where ?̅ is the sample
mean.

The average number of customers arriving at a bank branch is
eight per hour. Assume that customer arrivals follow a Poisson
process. The bank opens at 9:00 am in the morning. Answer the
following questions accordingly.
a) What is the probability that the first customer will arrive
after 9:10 am?
b) Suppose that it is now 9:15 and the first customer has
arrived at 9:12 am. What is the probability that the second
customer will arrive after 9:25 am?
c)...

When people order coffee at the counter, they will either order
regular or decaffeinated. assume that 20% order decaffeinated and
80% order regular, and the orders are independent.
a.What is the probability that, among the next 10 customers,
exactly 3 order decaffeinated?
b.What is the probability that, among the next 10 customers, the
number that order decaffeinated is within one standard deviation of
the mean?
c. Suppose that regular costs $4 per cup and decaffeinated costs
$3 per cup. What...

Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at
a rate of one every 20 minutes and the average time it takes for a
car to proceed through their single wash station is 8 minutes.
Answer the following questions under the assumption of Poisson
arrivals and exponential service.
(a) What is the probability that an arriving customer will have
to wait?
(b) What is the average number of cars waiting to begin their
wash?
(c) What is the probability...

1. Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 6 customers
per hour or 0.1 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 54 customers per hour, or 0.9
customers per minute. Determine the...

I. Solve the following problem:
For the following data:
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6 n = 12
b) Calculate
1) the average or average
2) quartile-1
3) quartile-2 or medium
4) quartile-3
5) Draw box diagram (Box & Wisker)
II. PROBABILITY
1. Answer the questions using the following
contingency table, which collects the results of a study to 400
customers of a store where you want to analyze the payment
method.
_______B__________BC_____
A...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 9 minutes ago

asked 28 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago