# Huge Multi Part Prob + Stats question from past paper

• hb2325
So we can find the probability that at least 150 pages in the book are without misprints by finding the probability that a N(200*0.3,200*0.3*0.7) distribution is greater than or equal to 150, which is approximately 0.0009.(ii) Similarly, the number of misprints in a book of 200 pages follows a Poisson(200*0.3) distribution, which can be approximated by an N(200*0.3, 200*0.3) distribution. So we can find the probability that the book contains at most 50 misprints by finding the probability that a N(200*0.3, 200*0.
hb2325
A university department has 2 secretaries (labelled A and B) who do all the word processing
required by the department. The number of misprints on a randomly sampled
page typed by secretary i (i=A,B) has a Poisson distribution with Mean Ui independent
of the number of misprints on any other page, where Mean Ua = 0.3 and Mean Ub = 1.2.Assume that each page is typed entirely by a single secretary. Of the typing required
by the department, 75% is done by secretary A and 25% by secretary B.(a) Find the probability that a randomly sampled page typed by secretary B contains
more than 1 misprint. [2 marks](b) Calculate the overall proportion of pages produced by the department that contain
no misprints. [3 marks](c) Suppose that a randomly sampled page produced by the department is found to
contain 2 misprints. Given this information, calculate the probability that this
page was typed by secretary A, Hence which secretary is most likely to have typed
the page concerned? [5 marks] A book typed entirely by secretary A consists of 200 pages.
(i) Let X be the number of pages in the book that contain no misprints. Name
the (exact) distribution of X. Find approximately the probability that at
least 150 pages in the book are without misprints. [5 marks](ii) Find approximately the probability that the book contains at most 50 misprints
in total.Attempt At soultions:

a) Using P(x=K) = (e^-u* u^k)/k! , I get the probability for X=0, X=1 add them and subtract from 1?

b) 0.25* Prob X=0 from part 1 + same thing for Sec A * 0. 75

c) Conditional prob. I am happy with this one.

d) i) I think this is a normal distribution.

Now if its a normal distribution, mean number of errors per page = 0.3 so number of errors in 200 page will be 60.

But how do I find The prob of 150+151...200 :S I am very confused and would love some help as my exam is on wednesday!

Thanks!

Last edited:
(d)(i): A page either has a misprint or it does not. Since each page has misprints independently of any other page, the number of pages which have no misprints in a book of $n$ pages typed by Secretary A follows a $\operatorname{Bin}(n, e^{-U_A})$ distribution. For a large number of pages this can be approximated by an $N(ne^{-U_A},ne^{-U_A}(1 - e^{-U_A}))$ distribution.

## 1. What is the purpose of a "Huge Multi Part Prob + Stats" question on a past paper?

The purpose of these types of questions is to assess a student's understanding and application of probability and statistics concepts in a complex and multi-part problem. They often require the use of multiple equations and methods to solve and can be challenging for students.

## 2. How should I approach solving a "Huge Multi Part Prob + Stats" question?

It is important to carefully read and understand the question before attempting to solve it. Identify the given information and what is being asked, and then determine the appropriate equations and methods to use. It may also be helpful to break the question into smaller parts and tackle them one at a time.

## 3. What are some common mistakes students make when solving "Huge Multi Part Prob + Stats" questions?

Some common mistakes include misinterpreting the question, using incorrect equations or formulas, and making calculation errors. It is also important to pay attention to units and be consistent with units throughout the problem.

## 4. What tips can you give for improving my performance on "Huge Multi Part Prob + Stats" questions?

Practice is key when it comes to improving your performance on these types of questions. Make sure you have a strong understanding of probability and statistics concepts and familiarize yourself with different types of problems. Also, be sure to carefully check your work and use logical reasoning to verify your answers.

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Yes, there are many online resources and textbooks that provide practice problems and solutions for "Huge Multi Part Prob + Stats" questions. Additionally, working with a study group or seeking help from a tutor or teacher can also be beneficial in improving your skills in this area.

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