Week - 19 - Central Limit Theorem - Likelihood of sample Mean

Can someone confirm if this session ‘Likelihood of sample Mean’ has the right video ? I am not seeing Likelihood of Sample mean discussed in any of the sessions - or am i missing something ?

Hi @VivekSasidharan,
The video is correct, can you please check it once again?

Hi … Sorry my mistake…but I had the whole confusion because of the Final Question in the chapter…
IQ Population Mean = 82
IQ Population SD = 15 ( P Sd )
Samples = 100 (N )
So Sample SD = P Sd * sqrt(N)
Why are we doing P Sd / sqrt(N) ? Is this formula discussed in any chapter ?

I think I am missing some concept here. Could you please clarify the same ?

Hi,
Yes this is a part of the chapter. Please check the lectures where a try to prove CLT is attempted.
You can also refer to this thread, specifically the proof by @sanjayk.

Hi @Ishvinder - Its still not clear to me as to why different approach is used for solving similar questions. I think I might be missing some basic concept

Let’s start with the example discussed in lectures . Throwing Dice and what is the the probability that Sum of the Dice throws is > 40 for 10 throws
Here
Pop Mean = 3.5
Pop SD = 1.708
n = 10

Expected Value of Sample = 3.5 ( 35 * 10 )
Sample SD = 5.401 ( 1.708 * sqrt(10) )

So here Probability that the sum is > 40 is the area under the the Normal Distribution N(35, 5.401) where Probability > 40.

So z-score = (40.5 - 35) / (5.401 ) = 1.0183
Probability based on Z - score= P(x>40.5) = 1 - P(x<40.5) = 0.15426

From my point of view , this example is the same as the question regarding Budget going over 1,440,000.
But the solution given is different.

Please clarify if there is any difference in the Dice throw question and the Budget question which is resulting in different solution approach.

@Ishvinder - Any luck with the same ?

Hi @VivekSasidharan
Are you getting to the same answer by using both these approaches?

@Ishvinder - Yes I am getting the same answer of .00275 ( Probability corresponding to Z-score = 2 ).
But its still unclear to me how this question is different from the IQ question.
When should we use the solution approach of the IQ question and when should we use the approach similar to the Dice Throw.

Yes, note that we can have multiple ways to solve q problem. The matter of fact that we get to same answer using qny of the methods rules out the possibility of being wrong at any point.