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 
(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 
(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 
(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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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.
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.
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
and can guide me with how to write a methodologi and conclusion?
and can guide me with how to write a methodologi and conclusion?
Can’t help you on this. 😀
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
can give abit longer or clear explaination?
Hi. Please google for more info. 😀
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
sir, for question 1c) only ai) and aviii) are bell shaped?
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.
thanks sir