Maths p6 normal distribution.. :(

[mominzahid]

Hey guys i need help i have my p6 on the 24th and i really have problems solving normal distribution questions. :/
I dont know when to apply limits in a normal distribution and i dont understand when we subtract the calculated probability through z-score from 1. Also if anyone has notes on this topic which cover the syllabus points and the points stated above please share..
im really tensed abt the exam since my p1 didnt go as expected.
Please help guys

 

[Rashmit Arora]

Hey guys i need help i have my p6 on the 24th and i really have problems solving normal distribution questions. :/
I dont know when to apply limits in a normal distribution and i dont understand when we subtract the calculated probability through z-score from 1. Also if anyone has notes on this topic which cover the syllabus points and the points stated above please share..
im really tensed abt the exam since my p1 didnt go as expected.
Please help guys

You use limits when you approximate a Binomial Distribution to a Normal Distribution. ~continuity corrections

Check out this website. It'll help for sure. - http://www.examsolutions.co.uk/

Cheers!

 

[mominzahid]

You use limits when you approximate a Binomial Distribution to a Normal Distribution. ~continuity corrections

Check out this website. It'll help for sure. - http://www.examsolutions.co.uk/

Cheers!

Hi there.. thanks alot for the website it really did clear up some of the basic concepts of this topic. however i still cant figure the whole continuity thing and when to apply it. also what is the difference b/w binomial distribution and normal distribution? :/

look at the question i uploaded for example. how do i know i have to apply limits in this question?
Can u please explain this question to me? also if there is any tutorial on continuity please tell me.. it'd really help me alot. Thanksss..

 

[Jaf]

Hi there.. thanks alot for the website it really did clear up some of the basic concepts of this topic. however i still cant figure the whole continuity thing and when to apply it. also what is the difference b/w binomial distribution and normal distribution? :/

look at the question i uploaded for example. how do i know i have to apply limits in this question?
Can u please explain this question to me? also if there is any tutorial on continuity please tell me.. it'd really help me alot. Thanksss..

Memorize this rule: Use end correction whenever you're changing from binomial distribution to normal distribution. That is, wherever you use normal approximation. (like in the question below)

Probability of getting an underweight apple = 2/15
Therefore, p = 2/15, q = 13/15 (where q is the probability of NOT getting an underweight apple; we get it by 1-p)

We're choosing apples from a random sample of 200 apples. So n = 200.
We now know X ~ B (200 , 2/15)
[this is read as: variable 'X' follows binomial distribution with parameters 200 (trials) and 2/15 (probability)]

We want the probability of getting more than 21 and less than 35 underweight apples.
So P(21<X<35) = ?

If you were to apply the binomial theorem here, your calculation would be accurate but it would become tedious and there is a chance you'd make an error. (try doing it if you don't get why)
So you use normal approximation here.
Check is np and nq are greater than 5 (as that is a condition that needs to be fulfilled before we can normally approximate)
np = 80/3 , nq = 520/3 (both are greater)

Let's take a new variable 'V'.
V ~ N (np , npq)
[this is read as: variable 'V' follows normal distribution with parameters np (mean) and npq (variance)]
Put in the values of np and npq.
V ~ N (80/3 , 208/9)

Now comes the continuity correction. We can't write P(21<V<35). Every time a variable is greater than a number, you add 0.5 to it. Just remember this and you'll easily remember the argument for < and ≥ will be the converse (that is you'll have to subtract for 0.5 for these signs).
So we need to find P(21+0.5 < V < 35 - 0.5) = P(21.5<V<34.5)
Standardize it. Z ~ N (0,1)
Put in the formula, Z = (V - mean)/square root of variance)
I can't show that here because of the lack of proper signs. :S

If you do this correctly, you'll get P(-1.075<Z<1.629).
This is = P(Z<1.629) - (1 - P(Z<1.075)) = 0.9483 - 1 + 0.8589 = 0.807!!
(yes, there's immense joy when you get a sensible answer in normal distribution )

 

[Rashmit Arora]

haha, thanks for explaining it to him, saved me time!

And the joy bit - i so agree.

 

[mominzahid]

Memorize this rule: Use end correction whenever you're changing from binomial distribution to normal distribution. That is, wherever you use normal approximation. (like in the question below)

Probability of getting an underweight apple = 2/15
Therefore, p = 2/15, q = 13/15 (where q is the probability of NOT getting an underweight apple; we get it by 1-p)

We're choosing apples from a random sample of 200 apples. So n = 200.
We now know X ~ B (200 , 2/15)
[this is read as: variable 'X' follows binomial distribution with parameters 200 (trials) and 2/15 (probability)]

We want the probability of getting more than 21 and less than 35 underweight apples.
So P(21<X<35) = ?

If you were to apply the binomial theorem here, your calculation would be accurate but it would become tedious and there is a chance you'd make an error. (try doing it if you don't get why)
So you use normal approximation here.
Check is np and nq are greater than 5 (as that is a condition that needs to be fulfilled before we can normally approximate)
np = 80/3 , nq = 520/3 (both are greater)

Let's take a new variable 'V'.
V ~ N (np , npq)
[this is read as: variable 'V' follows normal distribution with parameters np (mean) and npq (variance)]
Put in the values of np and npq.
V ~ N (80/3 , 208/9)

Now comes the continuity correction. We can't write P(21<V<35). Every time a variable is greater than a number, you add 0.5 to it. Just remember this and you'll easily remember the argument for < and ≥ will be the converse (that is you'll have to subtract for 0.5 for these signs).
So we need to find P(21+0.5 < V < 35 - 0.5) = P(21.5<V<34.5)
Standardize it. Z ~ N (0,1)
Put in the formula, Z = (V - mean)/square root of variance)
I can't show that here because of the lack of proper signs. :S

If you do this correctly, you'll get P(-1.075<Z<1.629).
This is = P(Z<1.629) - (1 - P(Z<1.075)) = 0.9483 - 1 + 0.8589 = 0.807!!
(yes, there's immense joy when you get a sensible answer in normal distribution )

haha, thanks for explaining it to him, saved me time!

And the joy bit - i so agree.

Thank you for ur help guys really it helped me so much it all is much clear now.. with ur help i have able to identify the major problem im facing..
that problem in i have serious trouble in identifying when to approximate from binomial to normal distribution.. take the question given above which u solved for example.. how do i know this is not binomially distributed but is normally distributed? :/
I know my questions sound totally stupid but my maths teacher didnt tell me most of this stuff so i have to seek help elsewhere.. and i have my p6 the day after tomorrow.. GOD HELP ME.. :'(

 

[hamza_sheikh182]

ey can anyone help me with this doubt

question 3 part 3..... how do we solve this?​

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