Question

The number of traffic accidents in a certain area follows a Poisson process with a rate...

The number of traffic accidents in a certain area follows a Poisson process with a rate of 1.5 per hour between 8:00 A.M. and 5:00 P.M. during the normal working hours in a working day. Compute the following probabilities.

  1. There will be no traffic accident between 11:30 AM to 12:00 PM.
  2. There will be more than 3 traffic accidents after 3:45 P.M.
  3. There will be in between 15 and 18 traffic accident during the normal working hours in a working day.
  4. The number of the traffic accidents during the normal working hours in a working day are within a S.D. from the mean.
  5. Find the median of the number of the traffic accidents during the normal working hours in a working day.

Homework Answers

Answer #1

1) expected number of accidents in 30 minutes between 11:30 AM to 12:00 PM =1.5*30/60=0.75

hence P( There will be no traffic accident between 11:30 AM to 12:00 PM )=P(X=0)=e-0.75*0.750/0! =0.4724

2)

expected number of accidents after 3.45 pm (in 1.25 hours)=1.5*1.25=1.875

hence There will be more than 3 traffic accidents after 3:45 P.M =P(X>3)=1-P(X<=3)=1- =0.121054

3)

number of expected accidents between 8:00 A.M. and 5:00 P.M (9 hours)=1.5*9=13.5

There will be in between 15 and 18 traffic accident = =0.285107

4)

here mean =13.5 and std deviation =√13.5 =3.674

hence 1 std deviation from mean values are =13.5-/+3.674 =9.826 to 17.174

hence P(9.826 <X<17.174)= =0.725614

5)

median of the number of the traffic accidents during the normal working hours in a working day =13

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The number of traffic accidents at a certain intersection is thought to be well modeled by...
The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.5 accidents per year If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution with a mean of 1.25. What is the probability of exactly three accidents occur in hour? What is the probability of less than two accidents in ten minutes? What is the probability that the time between two successive accidents is at least ten minutes? If ten minutes have gone by without an accident, what is the probability that an accident will occur in the...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution with a mean of 1.25. What is the probability of exactly three accidents occur in hour? What is the probability of less than two accidents in ten minutes? What is the probability that the time between two successive accidents is at least ten minutes? If ten minutes have gone by without an accident, what is the probability that an accident will occur in the...
The number of hits to a Web site follows a Poisson process. Hits occur at the...
The number of hits to a Web site follows a Poisson process. Hits occur at the rate of 1.9 per minute1.9 per minute between​ 7:00 P.M. and 9​:00 P.M. Given below are three scenarios for the number of hits to the Web site. Compute the probability of each scenario between .7:41 P.M. and 7:45 P.M. ​(a) exactly six. ​(b) fewer than six ​(c) at least six.
The number of hits to a website follows a Poisson process. Hits occur at the rate...
The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.9 per minute between​ 7:00 P.M. and 11​:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8 : 44 P.M. and 8​:46 P.M. Interpret each result. ​(a) exactly six ​(b) fewer than six ​(c) at least six
The number of hits to a website follows a Poisson process. Hits occur at the rate...
The number of hits to a website follows a Poisson process. Hits occur at the rate of 1.0 per minute between​ 7:00 P.M. and 12​:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7 : 29 P.M. and 7​:34 P.M. Interpret each result. ​(a) exactly eight ​ (b) fewer than eight ​ (c) at least eight ​ (a)​ P(8​)=___ ​(Round to four decimal places as​ needed.)
The number of hits to a website follows a Poisson process. Hits occur at the rate...
The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.1 per minute 2.1 per minute between​ 7:00 P.M. and 11​:00PM. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 10:44 P.M. and 10:50 P.M. Interpret each result. ​(a) exactly six ​(b) fewer than six (c) at least six (a) P(6)= _____ On about _____of every 100 time intervals between 10:44 P.M....
The number of hits to a website follows a Poisson process. Hits occur at the rate...
The number of hits to a website follows a Poisson process. Hits occur at the rate of 1.8 per minute between​ 7:00 P.M. and 9​:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7 : 43 P.M. and 7​:48 P.M. Interpret each result. ​(a) exactly eight ​( b) fewer than eight ​ (c) at least eight ​ (a)​ P(8​) =______ ​(Round to four decimal places as​ needed.)...
A particular report included the following table classifying 818 fatal bicycle accidents that occurred in a...
A particular report included the following table classifying 818 fatal bicycle accidents that occurred in a certain year according to the time of day the accident occurred. Time of Day Number of Accidents midnight to 3 a.m. 47 3 a.m. to 6 a.m. 52 6 a.m. to 9 a.m. 84 9 a.m. to noon 72 noon to 3 p.m. 79 3 p.m. to 6 p.m. 157 6 p.m. to 9 p.m. 193 9 p.m. to midnight 134 For purposes of...
A particular report included the following table classifying 712 fatal bicycle accidents according to time of...
A particular report included the following table classifying 712 fatal bicycle accidents according to time of day the accident occurred. Time of Day Number of Accidents Midnight to 3 a.m. 38 3 a.m. to 6 a.m. 27 6 a.m. to 9 a.m. 66 9 a.m. to Noon 77 Noon to 3 p.m. 98 3 p.m. to 6 p.m. 127 6 p.m. to 9 p.m. 164 9 p.m. to Midnight 115 (a) Assume it is reasonable to regard the 712 bicycle...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT