Question

The waiting time at a certain checkout counter follows an exponential distribution with a mean waiting time of five minutes.

a) Compute the probability that an individual customer waits longer than 5 1/2 minutes at the checkout counter.

b) Compute the exact probability that the average checkout time for 5 individuals is greater than 5 ½ minutes.

c) Compute the exact probability that the average checkout time for 15 individuals is greater than 5 ½ minutes.

d) Apply the Central Limit Theorem to approximate the probability that the average checkout time for 15 individuals is greater than 5 ½ minutes. How good is your approximation when n=15?

Answer #1

Suppose the waiting time at a certain checkout counter is
bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30 minutes.
a) Compute the mean waiting time at the checkout counter.
b) Compute the variance of the waiting time at the checkout
counter.
c) Compute the probability that an individual customer waits
longer than 5 1/2 minutes at the checkout counter.
d) Using...

Suppose the waiting time at a certain checkout counter
is bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30
minutes.
a) Compute the mean waiting time at the checkout
counter.
b) Compute the variance of the waiting time at the
checkout counter.
c) Compute the probability that an individual customer
waits longer than 5 1/2 minutes at the checkout counter.
d) Using...

Suppose the waiting time at a certain checkout counter is
bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30 minutes. a)
Compute the mean waiting time at the checkout counter. b) Compute
the variance of the waiting time at the checkout counter. c)
Compute the probability that an individual customer waits longer
than 5 1/2 minutes at the checkout counter. d) Using...

The waiting time (in minutes) for a new bitcoin block follows an
exponential distribution with? = 15.
a. What is the probability that no blocks are found within 30
minutes?
b. What is the probability that the waiting time for a new block is
between 10 minutes and 20 minutes?
c. What is the probability of finding less than 2 blocks in an
hour?

A customer spending waiting time at a place check-in counter is
a random variable with mean 8.2 minutes and standard deviation 1.5
minutes. Suppose that a random sample of n = 49 customers is
observed. Find the probability that the average time waiting in
line for these customers is:
(a) Less than 9.3 minutes
(b) Between 5 and 10 minutes
(c) Less than 7.5 minutes

The amount of time that a customer spends waiting at an airport
check-in counter is a random variable with mean 8.1 minutes and
standard deviation 1.6 minutes. Suppose that a random sample of
n=50 customers is observed. Find the probability that the average
time waiting in line for these customers is
(a) Less than 10 minutes
(b) Between 5 and 10 minutes
(c) Less than 6 minutes
Round your answers to four decimal places (e.g. 0.9876).

Suppose that the checkout time at a grocery store is an
exponential random variable with mean 3 minutes. Estimate the
probability that a cheker will serve more than 82 customers during
a 5 hour shift

Pete's Market is a small local grocery store with only one
checkout counter. Assume that shoppers arrive at the checkout lane
according to a Poisson probability distribution, with an arrival
rate of 15 customers per hour. The checkout service times follow an
exponential probability distribution, with a service rate of 25
customers per hour. The manager’s service goal is to limit the
waiting time prior to beginning the checkout process to no more
than five minutes. Also the manager of...

Dan's Store has installed a self-service checkout counter, and
wishes to understand how this has affected customer service.
Shoppers arrive on average the rate of one every other minute
(Poisson distribution). Each shopper takes an average of 82 seconds
to use the checkout, and that time is exponentially
distributed.
a.
Calculate how long it takes, on average, for a shopper at the
self-service counter, including how long they wait in line and how
long it takes them to do their...

The amount of time that a customer spends waiting at an airport
check-in counter (X) is a random variable with
mean 8.2 minutes and standard deviation 2.5 minutes. If a random
sample of n = 30 customers were observed, then
what is the probability that the sample average waiting time
exceeds 9 minutes? Show your work.

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