Question

at call center, calls come in at an average rate of four calls per minute. Assume that the time elapsed from one call to the next has the exponential distribution, and that the times between calls are independent.

a. find the prob. that after a call is received, the next call occurs in less than 10 sec.

b. Find a 95% confidence interval for the number of calls in a minute.

Answer #1

A call center in Perth, Australia receives an average of1.3
calls per minute. By looking at the date, a Poissondiscrete
distribution is assumed for this variable. Calculateeach of the
following
.a. The probability of receiving no calls in the firstminute of
its office hours.
b. The probability of receiving 1 call in the first minute.
c. The probability of receiving 3 calls in the first minute.

A call centre receives, on average, 10 calls per minute. The
highest number of calls received in any minute is 15. For any
randomly selected minute, find the probability that they will
receive:
i. At least 13 calls
ii. At most 2 calls
iii. 7 to 9 calls
iv. Find the Mean, Variance and Standard Deviation of the
distribution
show all working

On average ten phone calls arrive at a customer service call
center per minute during a specified time of day. Assume all calls
happen independently of each other.
In any given minute, determine the probability that the call
center receives exactly eight phone calls that minute. (to 4
decimals)

The emergency telephone (911) center in a large city receives an
average of 120 calls per hour during a typical day. On average,
each call requires about 121 seconds for a dispatcher to receive
the emergency call, determine the nature and location of the
problem, and send the required individuals (police, firefighters,
or ambulance) to the scene. The center is currently staffed by 4
dispatchers a shift but must have an adequate number of dispatchers
on duty and it has...

A telephone switchboard handles on the average 4 calls per
minute. If the calls follow a Poisson distribution, what is the
probability of:
(a) exactly 8 calls per minute, more than 10 calls per
minute?
(b) a call comes in with the next 30 seconds?
(c) assuming no call comes in during a 30 second period, what is
the probability that a call comes in the following 30 seconds?
(d) Using the Central Limit Theorem, how many calls can we...

Telephone calls arrive at a 911 call center at the rate of 12
calls per hour.
What is the mean number of calls the center expects to receive
in 30 minutes?
What is the standard deviation of the number of calls the center
expects to receive in 30 minutes? (Round your answer to two decimal
places.)
Find the probability that no calls come in for 30 minutes.
(Round your answer to five decimal places.)

The
time between telephone calls to a cable televisiom service call
center follows an exponential distribution with a mean of 1.5
minutes.
a. What is the probability that the time between the next two
calls will be 48 seconds or less?
b. What is the probability that the between the next two calls
will be greater than 118.5 seconds?

A simple random sample of 48 calls is monitored at an in-bound
call center and the average length of the calls is 8 minutes. The
population standard deviation σ is unknown. Instead the sample
standard deviation s is also calculated from the sample and is
found to be 4 minutes.
(9
marks)
Construct a 99% confidence interval (using the t-distribution)
for the average length of inbound calls.
What is the margin of error at the 95% confidence level?
Do...

A customer service center in Gary, Indiana receives, on average,
3.5 telephone calls per minute. If the distribution of calls is
Poisson, what is the probability of receiving more than 4 calls
during a particular minute? Do not round intermediate calculations.
Round your final answer to four decimals. Format for probabilities:
0.0000

Q1.(15) At one call center, assume the probability of receiving
one phone call in a given time period is the same, and the numbers
of phone calls in one time period is independent from others. It is
known that the average number of phone calls in any one hour is 10.
One hour period is randomly selected.
1.(5) Find the probability that exactly 11 phone calls will be
received.
2.(5) Find the probability that at most 8 phone calls will...

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