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Discussion –

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Discussion –

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# STPM 2015 Mathematics (M) Term 2 Assignment  ## 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.

(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.

(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.

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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.

1. Can you tell me what formulas you used in EXCEL? I have downloaded your excel file. My teacher want the table in vertical form.

• Hi. Are you my student? Please come to see me after class tomorrow.

• Nope. I found this website. Can I ask for the formulas question 1 (c) in excel? Please.

• Hi. Please try to use this formula

=NORMDIST(B25,$B$21,SQRT($B$22),TRUE)-NORMDIST(B24,$B$21,SQRT($B$22),TRUE)

• THANKSSSSSSSSSSSSSS !!!

• Sir may I know the answer for 2(c)? Is it 15 and 19? Both are bell shaped?

• Those more than 10 should be bell shaped.

2. 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.

3. 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 ? 🙂

• Hmmm. Approximation in probability distributions

4. and can guide me with how to write a methodologi and conclusion?

5. and can guide me with how to write a methodologi and conclusion?

• 6. 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

• Binomial : np>5, nq>5
Poisson : lambda>10

7. can give abit longer or clear explaination?

• 8. Hai kk lee.. Do you have a tuition centre for stpm student ?

• 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

9. sir, for question 1c) only ai) and aviii) are bell shaped?

• • 