3. Suppose 300 misprints are distributed randomly throughout a book of 500 pages.(a) Find the probability that a given page contains 2 or more misprints.(b) Approximate your answer in part (a) by using the Poisson approximation.

Given information Number of misprint pages=300 Number of page=500

Answered: Suppose 300 misprints are distributed…

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

Suppose that 20% of the people in a large city have used a hospital emergency room in the past year. If a random sample of 120 people from the city is taken approximate the probability that more than 24 used in emergency room in the past year. Use the normal approximation to the binomial with a correction for continuity.
2) The number x of people admitted to an intensive care unit in a particular hospital, on any given day, has a Poisson probability distribution with mean equal to five (5) people per day. What is the probability that the number of people admitted to an intensive care unit on a particular day is three (3)? Solve using Poisson's formula (Mendenhall et al., 2015).
According to American Airlines, Flight 215 from Orlando to Los Angelas is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to approximate the probability that exactly 130 flights are on time.
Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.
Suppose that a pair of fair dice are rolled 120 times. Let X be the number of rolls on which the sum of the two numbers is 12. Show your working details. You may use R to verify your answer. (a) Find the probability when X = 3 approximately using Poisson approximation. (b) Compute the actual probability from binomial distribution. Comment on the accuracy of Poisson approximation.
2. Cytomegalovirus (CMV) is a (generally benign) virus that infects one – half of young adults. If a random sample of 10 young adults is taken, find the probability that between 30% and 40% (inclusive) of those sampled will have CMV. Use the normal approximation with the continuity correction.
(b) Suppose the number of customers at a Sushi outlet is Poisson distributed where an average of nineteen customers are served per 30 minutes. (i) Over a fifteen-minute period, how many customers are served on average? Find the probability of exactly seven customers served over a fifteen-minute period. Write your answer correct to 4 decimal places. (iii) Calculate the probability at least 1 customer is served over a fifteen-minute period. Write your answer correct to 4 decimal places.

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

Suppose 300 misprints are distributed randomly throughout a book of 500 pages. (a) Find the probability that a given page contains 2 or more misprints. (b) Approximate your answer in part (a) by using the Poisson approximation.