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 24thand the 25th kids is more than 2 days?c. Find mean and the variance of the time needed to have 50 adult immigrantsin the territory.

Given: X ~ Poisson(2*40%) => X ~ Poisson(0.8)

Answered: Suppose people immigrate into a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

What is the answer
The number of calls made by a telemarketer follows a Poisson distribution with a mean of 2 calls in one minute. Find the probability that the telemarketer makes at most 8 calls in 3 minutes. Round to 4 places.
4. The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes. What is the probability that there are no calls within a 30-minute interval?
The number of substances produced by a radioactive breakdown shows a Poisson distribution with a mean of 25. Use the Poisson distribution to find the probability that the number of substances occurring in 1 second is between 23 and 27.
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
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?
Assume that your aunt wrote 139 letters to her family members in 2019. Let the random variable x represent the number of these letters that she wrote on a given day. Assume also that this scenario has a Poisson distribution. What is the mean number of letters written per day? Round to 3 decimal places. What is the standard deviation? Round to 3 decimal places.
Officer Thompson of the Bay Ridge Police Department works the graveyard shift. He averages 4.5calls per shift from this dispatcher. Assume the number of calls follows a Poisson distribution. Find theprobability that Officer Thompson get fewer than 2 calls in a shift.
Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute:Find the probability of 8 customers or less arriving within a minute. Find the probability of more than 7 customers arriving within a minute. Find the probability of 3 customers arriving within a minute.
Be a cafeteria with only one attendant. The rate of customer arrivals follows a Poisson process with an average of 10 customers per hour. The service time is exponentially distributed with an average time of 4 minutes. What is the probability of forming a queue, the average queue length and the average waiting time in the queue?
The random variable x represents the number of emails a student receives on a day. Assume it has a Poisson distribution with a mean of 14.3 emails. Find the probability that in a random day the student receives 3 emails. Round your answer to four decimal places.

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS