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Discussion – 

59

Discussion – 

59

STPM 2015 Mathematics (T) Term 3 Assignment

STPM 2015 Term 3 Mathematics T Assignment

Introduction

Binomial distribution may be approximated, under certain circumstances, by Poisson distribution, or normal distribution. One practical advantage is that the calculations for finding probabilities are much less tedious to perform.

Okay. Let me post this STPM 2015 Term 3 Mathematics (T) Coursework sample solution. before my holiday. 😀 No any comments will be replied until i am back from my holiday. Thanks. You still can leave any comment and i will review the comment as soon as possible. Remember, all the below are my personal opinions, please ask your school teachers for confirmation. I help you and you help others. Please share the information from your teachers too. Cheers.

Sample Question

Binomial distribution may be approximated, under certain circumstances, by Poisson distribution or normal distribution. One practical advantage is that the calculations for finding probabilities are much less tedious to perform.

1. Consider a random variable having binomial distribution B(n, p).

(a) Let p=0.05 and n=5, 10 and 20. Tabulate all the probabilities using binomial distribution, Poisson distribution and normal distribution. (Note: For n=5. manual calculations must be used)

(b) Repeat step 1(a) for p = 0.1 and 0.5.

 

2

(a) Illustrate graphically the probability distributions.

(b) Compare the probability distributions obtained and discuss your findings.

3. Investigate what happens when n increases.

Sample Solution for n=5, p=0.05

For binomial distribution B(n,p) where n=5, p=0.05, below are the sample calculations for using the binomial distribution, Poisson distribution, and normal distribution.

Remark. For normal distribution’s calculation above, the total probabilities are 0.9381, so i will suggest you add another 0.0619 to the probability for x=0. So that the total can be 1.00. Please ask your teacher and let me know. 🙂

Sample Graph

Graphs of binomial and Poisson distributions based on the above table. You should construct similar graph for normal distributions.

Sample Solution for n=10, p=0.05

For binomial distribution B(n,p) where n=10, p=0.05, below are the sample tables and graphs for the distributions. Please do the calculations yourself.

Sample solutions for others

For n=20, p=0.05

For n=5, p=0.1

For n=5, p=0.5

For n=10, p=0.1

For n=10, p=0.5

For n=20, p=0.1

For n=20, p=0.5

 

For non KK LEE students, please do yourself.

 

For KK LEE students, please do yourself and visit the students corner at kkleemaths.com for downloadable excel file of all the tables and graphs for reference. We will discuss in class soon. There are two versions of excel files. The latest updated excel file contains tables and graphs which are combined together. Cheers.

Comparison for p=0.05 (different values of n)

The shapes of the Poisson distribution and the binomial distribution are similar for p=0.05.

The graphs are not symmetrical an skewed to the left. So normal approximation are not suitable in these cases. When n increases, the distributions for p=0.05 are also skewed to the left. When the n is more than 100, the binomial distributions are almost symmetrical. The shape of binomial distributions tends to symmetrical as the n increases after n=100.

Comparison for p=0.1 and 0.5 (different values of n)

Please do yourself. Construct the graphs and see and investigate.

** For p=0.5, as n increases, the shape of binomial distribution is always symmetrical.

** You can try to make conclusion about the conditions for normal approximations(np>5, nq>5) and Poisson approximations(small p).

I will list down all the requirements from all the school teachers that i received here. Please share. Cheers

** Do for p=0.9

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KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

59 Comments

  1. Boi boi

    Dear sir,for example n =20, do we need calculate untill p(x=20)..and how many significant number we should take?

    Reply
    • KK LEE

      Hi. It depends on your teacher. For me, YES!

  2. cheng shen sing

    Sir, for the graph, you said do the calculation but what is that calculation you mean? Can you give me some hints about Q2b and 3

    Reply
    • KK LEE

      You need to show all the calculations(or workings) to obtains the probabilities.

    • cheng shen sing

      Not really understand. Can explain more?

    • KK LEE

      Similar to the calculation for n=5 and p=0.05. Please use the formula to find all the probabilities.

  3. Question mark?

    Sir, can I use smooth line graph instead of bar graph?

    Reply
    • KK LEE

      Vertical line

  4. Afiqah

    Sir,how to compare the graph if I do 3 probabilities(binomial,poisson,normal) in one graph ?

    Reply
    • KK LEE

      Compare their shapes

  5. Wan

    sir,how to do Q2b and Q3? because i not really understand.

    Reply
    • KK LEE

      Please refer the above

  6. V

    Sir, for the normal distribution involving n=5 and p=0.05,
    since usually normal distributions involve P(Xx), using P(X=x) = P(x-0.5<X<x+0.5) would naturally mean using normal distribution as an approximate for binomial distribution..so maybe that is why it is off by 0.0619
    still, for this question, we can't do using normal distribution..so we have to use the continuity correction method, correct?

    Reply
    • KK LEE

      Yes

    • V

      Oh, ok..thank you sir

    • MAVIS

      sorry sir, I want to ask why we can use continuity correction in 1(a)-normal distribution? because the np and nq we found all less than 5 but the condition of continuity correction is used when np and nq greater than 5.

    • KK LEE

      That’s why the result will show you the normal approximation is not suitable.

  7. tiya

    sir, i dont quite understand the calculation for the normal distribution part. why is the x is between -0.5 and 0.5

    Reply
    • KK LEE

      Continuity correction.

  8. Jakiro

    Sir, may i ask the purpose of adding another 0.0619 to the probability for x=0 (Normal distribution). That won’t be the correct value for P(X=0) isn’t it ?

    Reply
    • KK LEE

      What i mean is if your school teacher wants the addition, then you add the values. Else, leave it there.

    • Jakiro

      Alright, thank you sir

  9. keown

    do we need to show normal distribution graph ?

    Reply
    • KK LEE

      It depends on your teacher

  10. Low Sie Hui

    So i need to calculate to n=100 to investigate what happens when n increase?

    Reply
    • KK LEE

      It depends on your teacher. For me, yes

  11. Anonymous

    Sir, can i know how to do the conclusion?? Thank you sir

    Reply
    • KK LEE

      No comment. Thanks

    • yy

      graph for p=0.05 should be skew to right isnt it?

    • KK LEE

      ya

  12. Band 6 Muet

    Hi sir, are you sure that the graphs are skewed to the left? Shouldn’t they be skewed to the right as more data is on the left side?

    Reply
    • KK LEE

      You can edit yourself

  13. Ang

    Sir, how to compare probability distribution ? Isn;t explain difference of the graph?? What is meant by discussion your finding from the question???

    Reply
    • KK LEE

      Please ask your school teacher what he/she wants. Basically is explain the difference between the graphs.

  14. Ellene

    sir, may i know how to compare the probability distributions obtained? what should i write in these question?

    Reply
    • KK LEE

      Please ask your school teacher what he/she wants. Basically is explain the difference between the graphs.

    • Ellene

      ok..thankq sir..
      ehmm..for the question when n increase, we need to use any bigger value of n do with different value p?

    • KK LEE

      It depends on your teacher

  15. Ang

    sir, why the graph is bar not vertical line??

    Reply
    • KK LEE

      You can always change to any shape you like.

  16. Stich

    Sir, since we are doing n=5 , p=0.1, after that we are also doing n=10 p=0.1, will the first five readings be the same in n=10 for binomial..

    Reply
    • KK LEE

      No

  17. Jeccy

    Sir , may i know that why i calculate the binomial distribution for n=20 p=0.05 by using computer , and the result showing is negative ?

    Reply
  18. Puvaneshwaraan

    Sir , how many graph should i plot??

    Reply
    • KK LEE

      It depends on your teacher.

  19. boon

    Sir, question 3 need to draw combine graph??

    Reply
    • KK LEE

      Hmm.. It depends on your teacher. For me, no.

  20. BAND 5 MUET

    Sir how to write the methodology? pls help

    Reply
    • KK LEE

      Hi. Please refer your school teacher.

  21. nbk

    is the bar graph suitable for binomial,poisson and normal distribution ??can use line graph or not??

    Reply
    • KK LEE

      You can use any graphs. Line or bar or curve. It depends on your school teacher.

  22. Apple

    Hi Sir, what we need to compare for 2(b)? we need to compare between binomial, poisson and normal or comapre within binomial/ poisson/ normal (ex: when n is fixed and p changes from 0.05 to 0.5)?

    Reply
    • KK LEE

      Yes. Compare everything. Or you can refer to your teacher

  23. ZZ

    Excuse me, sir. May I know do i need to use manual calculation for p=0.1 and n=5? and also p=0.5, n=5

    Reply
    • KK LEE

      It depends on your teacher.

  24. Lee

    Hello sir. As I do the calculation for larger number of n, the value I get is getting smaller, until 1*10^-9. In this case, should I state the answer as ”0” or express the number in standard form?

    Reply
    • KK LEE

      It depends on your teacher.

  25. afiza

    sir, if how much significant figures do i need for all the values?
    is four is 4 s.g.f is ok?

    Reply
    • KK LEE

      It depends on your teacher.

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