Question

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

Answer #1

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?...

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...

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...

1)During the period of time that a
local university takes phone-in registrations, calls come in at the
rate of one every two minutes.
a.Clearly state what the random
variable in this problem is?
b.What is an appropriate distribution
to be used for this problem and why?
c.What is the expected number of calls
in one hour?
d.What is the probability of receiving
three calls in five minutes?
e.What is the probability of receiving
NO calls in a 10-minute period?
f.What...

Assume that the number of telephone calls arriving at a
switchboard by time t (minutes) is described by Poison
process {N(t)}. On average, one call comes in every 10
minutes.
Given that exactly one call arrived in 0 < t ≤ 15,
calculate the conditional probability that at least one call will
arrive in 15 < t ≤ 20.

Assume that the number of telephone calls arriving at a
switchboard by time t (minutes) is described by Poison
process {N(t)}. On average, one call comes in every 10
minutes.
Calculate the probability that no calls will occur between 0
< t ≤10 and that exactly one call will occur in 10 <
t ≤ 15.

A toll-free phone number is available from 9 a.m. to 9 p.m. for
your customers to register complaints about a product purchased
from your company. Past history indicates that an average of 0.3
calls are received per minute. Complete parts (a) through (d). a.
What properties must be true about the situation described here in
order to use the Poisson distribution to calculate probabilities
concerning the number of phone calls received in a? 1-minute
period? Select all the assumptions for...

For a six-month period, an airline had on-time departures 84%
of the time and on-time arrivals 79% of the time. (These
statistics were based on tracking a sample of scheduled flights,
not all scheduled flights.) Suppose you had taken three flights on
the airline in that period.
a) What is the probability that all three were on-time
departures?
b) What is the probability that none were all-time
departures?
c) What is the probability that at least one was an on-time...

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