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Excuse me, sir.
I think we have a small matter in Example 3:
50% of 95% must be equal to 47.5% (0.475 => z= 1.96).
Length = 1.96 x 0.2 = 0.392
X = 10 – 0.392 = 9.608
So, there is a 95% probability that the length will be more than 9.608 cms.
Please help us re-check, sir.
Thank you so much.
please how did you get the z as 1.645
By working backwards through the tables. 1.64 gives a result of 0.4495, 1.65 gives a result of 0.4505.
So to get 0.45 (45%) it is between 1.64 and 1.65.
i thought the z score answer in the normal distribution table represents the area lying to the left of the given X value
It is to the left or to the right because the curve is symmetrical.
Sir, if Z = (x – x bar) / S.D.,
in the eg. 2 (c) part the answer should come like this nah,
(9.8 – 10) / 0.2 = -1 because the x is 9.8 and xbar is 10..
Am I correct????
Yes, but it doesn’t matter if it is positive or negative because the curve is symmetrical. Therefore the sign does not matter.
ok thank u sir
You are welcome 馃檪
Hey John, in example 2, shouldn鈥檛 the 50% of 10 cms be 5, or am I doing something wrong?
50% of 10cm is indeed 5cm, but that is not what the question is asking for.
It is asking what proportion of all the units will have a length of 10cm, and because 10cm is the average it means that half (50%) of the units are longer than 10cm, and half of them are less than 10cm.
sir in the exam. if the answer is fill in the blanks. should we write it as a percentage or decimal?
It will be made clear which is required 馃檪
what if the Arithmetic mean was say 14 would we still say it is 50% more if the question was to find a proportion more than 14?
Yes. The curve is symmetrical about the mean and so the proportion more (or less) than the mean is always 50%.
Thank you sir for the lecture. Why doesn’t this chapter and the last chapter have practice questions?
This is new to me and I would love to exercise it a bit more please
I will add questions at some stage. However you will find lots of questions in your Revision Kit (and it is essential that you get a Revision Kit from one of the ACCA Approved Publishers 馃檪 )
Sir, in example 2 (b) if the question asked us to find proportion having length more than 10.4 cm would we have done:
0.5 – 0.4772 ?
Yes we would 馃檪
In what cases do we subtract the probability from 0.5?
When we are looking for the probability of being above or below a certain value (as I show in my free lectures).
Greetings sir,
I feel the answer should have been calculated by adding the z to the mean, and not subtracting it.
z = (x – xbar)/sd
1.645 = (x – 10) / 0.2
1.645×0.2 = x – 10
0.329 = x – 10
0.329 + 10 = x
10.329 = x
If you are referring to example 3, then that cannot possibly be the answer.
There is a 50% chance of being more than 10, so how can there possibly be a bigger chance of it being more than 10.329? It would make no sense at all.
The algebra of the formula shows another answer as demonstrated. If you don鈥檛 agree, how do you reply to the working I showed you ?
Perhaps we could say, that 50% chance there is of it being below 10 – as it is above as the distribution is symmetrical, and then we apply the first 50% to below 10, and the balance of the probability of the 95%, ie 45% to above the 10.
In the end, shouldn鈥檛 the interpretation of the probability distribution be subject to the formula calculation ?
Awaiting your reflection and suggestion.
Thankyou.
You cannot learn this just as playing with algebra.
Draw the curve in the way that I do in my lecture – the answer could not possibly by 10.329 as I wrote before.
So that means if theres 50% more chances that its more than 10cm then in that case the formula would be
Z=10-x divide by 0.2
?
As I wrote before, there is no point whatsoever in simply learning formula without understanding.
The z value is the different between the mean and the point being considered, divided by the standard deviation.
Because the curve is symmetrical it is irrelevant when calculating the z value whether the point being considered is more or less than the mean.
the application used to derive the algebraic expression is wrong. we know that 50% is above the mean. and the probability than the length will be more than X is 95%, meaning that the point x is bellow 10cm and in the expression for the Z score you need to subtract the X from the average (10cm)
Z =(10-x)/0.20
where z=1.645
1.645=(10-X)/0.20
1.645*0.20=10-X
0.329 = 10-X
X=10-0.329
X=9.671
which is same as the lecturer
A new topic for me, but you explained it so well as always. I was so confused initially reading the example questions but had a few “aha moments” during the lecture. So thank you for helping me to get my head around it. 馃檪
Thank you for your comment 馃檪
sir,in determining the proportions of what is less than a mean(say 9.8 as in example2) can you work with the value directly by dividing with SD as done for those above and then change to standard form. like 9.8/0.2=49(4.9*10^1 then look up in the table just like in logarithms and indices).
No. You can only use the tables directly to find the proportion between the mean and some other value (here, between 10 cms and 9.8 cms).
Hi sir,
Please explain this questions.
Q1)A normal distribution has a mean of 75and a variance of 25.
what is the upper quartile of this distribution?
Q2)A normal distribution has mean of 150,and a standard deviation of 20.
80% of the distribution is below which of the following (approximately)?
In future please ask this kind of question in the Ask the Tutor forum, and not as a comment on a lecture.
For the first question you need to find the value that has a probability of 25% (0.25) of being above the mean.
For the second question you need to find the value that has a probability of 80 – 50 = 30% (0.30) below the mean.
In both cases you need to work backwards in the tables to find the number of standard deviations (the z score) in the way I explain in the lectures.
what if the z score for 10 and 10.4 is 2. 96
then the area from curve table that we would choose is 2.906 ‘s = 0 .4985 ?
Hi SIr,
Can you please explain again what you meant by area of bar is proportional to frequency.
I cant seem to understand it