Question

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 be
received.

3.(5) Find the probability that the number of phone calls will be
greater than the mean number of phone calls (in one hour).

Answer #1

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...

If a phone call is received once every 10 minutes on average,
during a one-hour interval,
1) The probability that exactly one phone call is received
during the first 30 minutes and exactly two calls in the last 30
minutes
2) The expected value of the distribution of the time of the
arrival of the first call
3) The probability that the second phone call is received
between 30-40 minutes
4) The probability that the third phone call is received...

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 number of telephone calls per unit of time made to a call
center is often modeled as a Poisson random variable. Historical
data suggest that on the average 15 calls per hour are received by
the call center of a company. What is the probability that the time
between two consecutive calls is longer than 8 minutes? Write all
probability values as numbers between 0 and 1.

Suppose the number of phone calls made by the customers of a
particular phone company in one hour is the random variable ? ~
???????(?), where ? > ? is known. Let ?? be the length of the ?
?? phone call, for ? = ?, ?, ⋯ , ?. Assume the ?? ′? are
independent of each other, and also independent of ?. Also assume
that ?? ~ ???????????(?), for all ?, where ? > ? is known.
Define...

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.

On the average, there is one new customer calling in to a call
center every 20 minutes. Assume the
number of calls follows the Poisson process.
(a) What is the probability that in the next 40 minutes, exactly 3
new customers will call?
(b) What is the probability that there are no calls in the next
hour?

4. Phone calls arrive at the rate of 48 per hour at the
reservation desk for Varig Airlines. a. Find the probability of
receiving three calls in a five-minute interval time. b. Find the
probability of receiving exactly 10 calls in 15 minutes. c. Suppose
no calls are currently on hold. If the agent takes five minutes to
complete the current call, how many callers do you expect to be
waiting by that time? What is the probability that none...

Phone calls arrive at the rate of 24 per hour at the reservation
desk for Regional Airways.
a. Compute the probability of receiving two
calls in a 10-minute interval of time.
(to 4 decimals)
b. Compute the probability of receiving exactly
12 calls in 15 minutes.
(to 4 decimals)
c. Suppose no calls are currently on hold. If
the agent takes 5 minutes to complete the current call, how many
callers do you expect to be waiting by that time?...

The phone lines to an airline reservation system are occupied
40% of the time. Assume that the events that the lines are occupied
on successive calls are independent. Assume that 10 calls are
placed to the airline. a. What is the probability that for exactly
three calls, the lines are occupied? b. What is the probability
that for at least one call, the lines are not occupied? c. What is
the expected numb

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