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STPM PBS Assignment

STPM Mathematics (M) Assignment

By KK LEE

March 16, 2015

STPM 2015 MM Term 2 PBS Question

It may be cumbersome and time consuming to determine the probability distributions for binomial and Poisson random variables. Under certain circumstances, normal distribution can be used to approximate these two discrete probability distributions. To use a continuous probability distribution to approximate a discrete probability distribution, continuity correction is necessary.

Question 1

(a) Determine the probability distribution for a binomial random variable, X, with parameters n and p in each of the following cases.
(i) n=10,p=0.1
(ii) n=10,p=0.2
(iii) n=10,p = 0.3
(iv) n=10,p=0.5
(v) n=20,p=0.l
(vi) n=20,p=0.2
(vii) n=20,p=0.3
(viii) n=20,p=0.5

(b) Plot the probability distributions obtained in part (a). Comment on the shapes of the distributions.

(c) Determine which of the probability distributions are bell shaped. In each of these cases, use the normal distribution with parameters $\mu= np$ and $\sigma^2 = npq$ to calculate P(x-0.5<X<x+0.5) where x=0,1,2,…,n.

(d) Suggest the condition under which the.binomial distribution can be approximated by the normal distribution.

Question 2

(a) Determine the probability distribution for a Poisson random variable, Y, with parameter $\lambda$ = 1, 3, 5,…,25.

(b) Plot the probability distributions obtained in part (a). Comment on the shapes of the distributions.

(c) Determine which of the probability distributions are bell shaped. In each of these cases, use the normal distribution with parameters $\mu= \lambda$ and $\sigma^2 = \lambda$ to calculate P(y-0.5<Y<y+0.5) where y=0,1,2,…

(d) Suggest the condition under which the Poisson distribution can be approximated by the normal distribution.

Sample Solution

I am not going to give you the full solution here. But i will share the excel file to help you to calculate all the probabilities.

Click here to download

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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.

22 Comments

Erlyu Yi on March 20, 2015 at 12:09 am

Can you tell me what formulas you used in EXCEL? I have downloaded your excel file. My teacher want the table in vertical form.
Reply
- KK LEE on March 20, 2015 at 12:28 am
  
  Hi. Are you my student? Please come to see me after class tomorrow.
- Erlyu Yi on March 20, 2015 at 1:49 am
  
  Nope. I found this website. Can I ask for the formulas question 1 (c) in excel? Please.
- KK LEE on March 20, 2015 at 4:52 pm
  
  Hi. Please try to use this formula
  
  =NORMDIST(B25,$B$21,SQRT($B$22),TRUE)-NORMDIST(B24,$B$21,SQRT($B$22),TRUE)
- Erlyu Yi on March 23, 2015 at 2:53 pm
  
  THANKSSSSSSSSSSSSSS !!!
- Erlyu Yi on March 23, 2015 at 6:38 pm
  
  Sir may I know the answer for 2(c)? Is it 15 and 19? Both are bell shaped?
- KK LEE on March 23, 2015 at 7:46 pm
  
  Those more than 10 should be bell shaped.
ruzainie on March 24, 2015 at 9:26 am

hye..good morning sir… i’m new maths m teacher for form 6. i would like to know more about u sir.. maybe u can teach me more about maths m because im fresh graduate.
Reply
fanny on March 25, 2015 at 6:46 pm

hey teacher , cani know how to create a title for this PBS ? im no idea for it ,,can u guide me with give me some example ? 🙂
Reply
- KK LEE on March 25, 2015 at 7:00 pm
  
  Hmmm. Approximation in probability distributions
fanny on March 25, 2015 at 6:47 pm

and can guide me with how to write a methodologi and conclusion?
Reply
fanny on March 25, 2015 at 6:47 pm

and can guide me with how to write a methodologi and conclusion?
Reply
- KK LEE on March 25, 2015 at 7:01 pm
  
  Can’t help you on this. 😀
fanny on March 25, 2015 at 9:38 pm

can u explain wat mean tat a condition under a poisson and binomial can be approximated to normal distribution? and a reason for the approximation to normal distribution > can give an example for me :} thx
Reply
- KK LEE on March 25, 2015 at 10:27 pm
  
  Binomial : np>5, nq>5
  Poisson : lambda>10
fanny on March 25, 2015 at 10:46 pm

can give abit longer or clear explaination?
Reply
- KK LEE on March 26, 2015 at 12:14 am
  
  Hi. Please google for more info. 😀
Nurul Fatin on March 28, 2015 at 7:36 pm

Hai kk lee.. Do you have a tuition centre for stpm student ?
Reply
- KK LEE on March 28, 2015 at 7:52 pm
  
  Hi. Yes. We have maths m tuition now. Every Friday 6.20 to 8.00pm. And we have term 2 intensive class. Every Friday 4.30 to 6pm
jennis on April 16, 2015 at 4:53 pm

sir, for question 1c) only ai) and aviii) are bell shaped?
Reply
- KK LEE on April 16, 2015 at 10:57 pm
  
  Normally, binomial distributions are bell-shaped if p is near to 0.5. You can see from the binomial graph. But the final answer is depends on your teacher.
- jennis on April 17, 2015 at 9:09 pm
  
  thanks sir