The number of requests for assistance received by a towing service is a Poisson process with...

Question

Question

The number of requests for assistance received by a towing service is a Poisson process with...

The number of requests for assistance received by a towing service is a Poisson process with rate θ = 4 per hour.

a. Compute the probability that exactly ten requests are received during a particular 2-hour period.

b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance?

c. How many calls would you expect during their break?

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

✔ Recommended Answer

Answer #1

Concepts and reason

The concept used to solve this problem is the concept of the using Poisson distribution for the events which are very less likely to happen.

The Poisson distribution is a discrete probability distribution which can be used to determine the probability of a given number of events occurring in a fixed interval of time. It can be used to model situations where the chances of the happening of events is very low.

Fundamentals

Poisson distribution has following conditions,

The first is 9{
U , that is, the number of trials is indefinite.

The second is 06d , which represents that the probability of success is small for each trial.

The third is np = 2 , which is finite, where is a positive real number.

Consider a random variable having mean rate of occurrences following a Poisson distribution. The probability distribution for the variable can be written as follows,

ix
2=(x=x)

Here is the parameter of the distribution which is equal to the mean of the distribution.

The probabilities of X = x instances of the event can be calculated by using the density function.

(a)

It is provided that the number of requests received by a towing service with per hour and. Let X be the probability that exactly 10 requests have been received during 2-hour period is calculated as,

X~P(2)
2=nxp
4x2

101
„(8)*, 0 =(01=x)d
1 m 2 =(x= x)

It can be calculated using Excel. The screenshot of the same is shown as,

=POISSON.DIST(10,8,FALSE)
D
E
0.09926153383

(b)

Let Y be the probability that they do not miss any calls during lunch break of half an hour. It is provided that n=4, p=0.5

Y - P(1)
a=nxp
= 4x0.5
= 2

(7)x_3 =(0=)d
vry a =((= 1)d

Using excel the probability is calculated and screenshot of the same

fx
=POISSON.DIST(0,2,FALSE)
0.13533528324!

(c)

The total number of calls they would expect during the break is calculated as,

2=nxp
= 4x0.5
= 2
Y - P(2)

Ans: Part a

The probability of 10 requests received during the 2-hour period P(X = 10) is 0.099.

Part b

The probability that they do not miss calls during lunch break of half an hour is 0.1353 .

Part c

The total number of calls they would expect during break is 2.

Add a comment

Answer 2

Similar Homework Help Questions

The number of requests for assistance received by a towing service is a Poisson process with...

The number of requests for assistance received by a towing service is a Poisson process with rate ? = 4 per hour. a) If the operators take a 30 min break for lunch, what is the probability that they do not miss any calls for assistance? b) Assuming they work 10 total hours on a particular day. What is the probability that assist less than 30 people (consider and approximation to help you solve this part)? c) Calculate the average...
3) The number of requests for assistance are received by a towing service at an average...

3) The number of requests for assistance are received by a towing service at an average steady rate of 4 per hour. If, during a normal day the requests are received independently of one another, compute the probability that exactly ten requests are received during a particular 2-hour period of a normal day. Suppose, that the dispatcher ignored at least one call between 225pm and 2:45pm. What is the probability that no more than one call was received during this...
Write bimomial or Poisson: A particulr telephone mber is used to moelve both volce calls and fat mesages. Suppose t...

Write bimomial or Poisson: A particulr telephone mber is used to moelve both volce calls and fat mesages. Suppose that 25% of the incoming all involve fx mesages, and consider a imple of 25 incoming calls. What is te probability d aAtmot 6 of tdhe calle olea fa mge Eaty 6 of the calls ivolve a fax mge? At ast 6 of de calle ivolve a farmge? 4 More than 6 of de cals ivelve a fa message? The mber...

Use Poisson Distribution to solve problems 6-7 6. The number of calls received by a car...

Use Poisson Distribution to solve problems 6-7 6. The number of calls received by a car towing service averages 1.25 per hour Use the Poisson distribution to find the probability that in a randomly selected hour the number o calls is 2. Show the result of probability calculations and circle one of the multiple choice answers. (6 points) A) 0.1865 B) 0.2238 C) 0.1586 D) 0.3524
The truck traffic on a certain highway can be described as a Poisson process with a...

The truck traffic on a certain highway can be described as a Poisson process with a mean arrival rate of 1 truck per minute. The weight of each truck is random and the probability that a truck is overloaded is 15% 43 What is the probability that there will be at least 2 trucks passing the weight station in a 10 min period Whr the eohubilior bweiehing station will overloaded? Suppose the weighing station will close for 30 min during...
1) The number of calls received at a certain information desk has a Poisson Distribution with...

1) The number of calls received at a certain information desk has a Poisson Distribution with an average of 6 calls per hour. (15 points) (a) Find the probability that there is at exactly one call during a 15 minute period. (You cannot use tables here - show all work) (b) Find the probability that at least 6 calls are received during a 30 minute period. (you may use tables here) ******************************** 2) Note that for the above problem, the...

The number of people arriving for treatment at an emergency room can be modeled by a...

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of four per hour.(a) What is the probability that exactly three arrivals occur during a particular hour? (Round your answer to three decimal places.)(b) What is the probability that at least three people arrive during a particular hour? (Round your answer to three decimal places.)(c) How many people do you expect to arrive during a 30-min period?people
Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such that,...

Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such that, λ(t)-0.5 calls/hr for 0<ts? hr, λ (t)-0.9 calls/hr for 7<ts17 hr, and λ(t)-1.3 calls/hr for 17<ts24. a. Find the probability that there are no calls between 6 am and 8 am. b. Find the probability that there are at most 2 calls before noon. c. What is the probability that there is exactly one call between 4:50 pm and 5:10 pm? d. What is...
3. Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such...

3. Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such that, λ (t)-0.5 calls/hr for 0<ts7 hr, λ(t)-09 calls/hr for 7<ts17 hr, and λ (t)-1.3 calls/hr for 17<ts24 a. b. c. d. Find the probability that there are no calls between 6 am and 8 am. Find the probability that there are at most 2 calls before noon What is the probability that there is exactly one call between 4:50 pm and 5:10 pm?...

4. (Lecture 25, Continuous Time Random Process, 9 pts) Suppose that the total number of requests...

4. (Lecture 25, Continuous Time Random Process, 9 pts) Suppose that the total number of requests to a web server received between time 0 and time t, N(t), is given by a Poisson random process with rate 2- 10 requests per minute (a) Find the probability that exactly 8 requests are received in the first 30 seconds. (b) Find the probability that exactly 8 requests are received in the first 30 seconds and that exactly 8 requests are received in...

The number of requests for assistance received by a towing service is a Poisson process with...

Homework Answers

Add Answer to:
The number of requests for assistance received by a towing service is a Poisson process with...

Post as a guest

Earn Coins