Q3/ If the number of accidents on the highway between Baghdad and Mosul Between 9 p.m. and 10 p.m. onFriday is a random variable having a Poisson distribution with mean 0.5 find the probability that there will be:a) Fewer than 3 accidents.b) Anywhere from 2 to 6 accidents, inclusive on this way between 9 p.m. and 10p.m on Friday.

Given: Mean number of accidents between 9pm to 10 pm λ=0.50 Let X be the number of accidents X ~…

Answered: Q3/ If the number of accidents on the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is the probability that he gets at least 2 wins? b) Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and suppose that P(X =0) = 0.02. i. What is the probability that at most one person enter the bank in one hour? ii. Determine the mean and standard deviation of X
2) The number of x people entering the intensive care unit (ICU) at a particular hospital on any given day has a Poisson probability distribution with mean rate of five persons per day. What is the probability that the number of people entering the ICU for 5 days is between 20 and 35 inclusive?
The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?
Suppose people immigrate into a territory at a Poisson rate of 2 per day. Assume that 40% of immigrants are adults and 60% are kids. a. What is the probability that 4 adult immigrants arrive in the next 3 days? b. What is the probability that the time elapsed between the arrival of 24th and the 25th kids is more than 2 days? c. Find mean and the variance of the time needed to have 50 adult immigrants in the territory.
8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. O a. .1901 O b. None of the above O C. .2075 O d. .3701 O e..1016 日田

The number of corner kicks in a 90 minute soccer game follows a Poisson distribution with a mean of 5. Then, the probability that there will be 3 corner kicks in 45 minutes is
The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page. What is the probability that the typist makes 3 errors on a page? What is the probability that a randomly selected page does not need to be retyped?
2. If electricity power failures occur according to a Poisson distribution with an average of 5 failures every 20 weeks, calculate the probability that there will not be more than one failure during a particular week.
4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
8. An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the fault is a Poisson random variable with A- 5. a) What is the probability that at most 3 cars per year will experience a catastrophe? b) What is the probability that more than 1 car per year will experience a catastrophe?
3. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. a). Find the probability that for 36 jets the average taxi and takeoff time is less than 8.33 minutes per plane. b). Find the probability that for 36 jets the average taxi and takeoff times is more than 8.55 minutes.
A certain model of an automobile is having a fault in the braking mechanism after sale. This is a very serious failure with catastrophic results at high speed. The distribution of the number of cars per year that will experience the fault is found to be a random variable with x=5. a) What is the probability that at most 3 cars per year will experience a catastrophe ? b) What is the probability that more than 1 car per year will experience a catastrophe ?

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS