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October 17, 2023 at 2:40 pm
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.
May 31, 2023 at 8:54 pm
please how did you get the z as 1.645
John Moffat says
June 1, 2023 at 7:33 am
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.
April 6, 2023 at 4:18 am
i thought the z score answer in the normal distribution table represents the area lying to the left of the given X value
April 6, 2023 at 9:29 am
It is to the left or to the right because the curve is symmetrical.
December 9, 2022 at 4:45 am
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????
December 9, 2022 at 8:39 am
Yes, but it doesn’t matter if it is positive or negative because the curve is symmetrical. Therefore the sign does not matter.
December 9, 2022 at 10:30 am
ok thank u sir
December 9, 2022 at 5:49 pm
You are welcome 🙂
November 12, 2022 at 3:29 pm
Hey John, in example 2, shouldn’t the 50% of 10 cms be 5, or am I doing something wrong?
November 13, 2022 at 8:30 am
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.
August 21, 2022 at 7:15 am
sir in the exam. if the answer is fill in the blanks. should we write it as a percentage or decimal?
August 21, 2022 at 9:50 am
It will be made clear which is required 🙂
December 22, 2021 at 7:47 am
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?
December 22, 2021 at 8:09 am
Yes. The curve is symmetrical about the mean and so the proportion more (or less) than the mean is always 50%.
July 28, 2021 at 12:25 pm
Thank you sir for the lecture. Why doesn’t this chapter and the last chapter have practice questions?
July 28, 2021 at 12:26 pm
This is new to me and I would love to exercise it a bit more please
July 29, 2021 at 8:23 am
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 🙂 )
May 24, 2021 at 7:51 am
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 ?
May 24, 2021 at 2:32 pm
Yes we would 🙂
September 12, 2022 at 2:00 pm
In what cases do we subtract the probability from 0.5?
September 12, 2022 at 4:19 pm
When we are looking for the probability of being above or below a certain value (as I show in my free lectures).
March 29, 2021 at 5:19 pm
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
March 30, 2021 at 7:34 am
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.
March 30, 2021 at 10:55 am
The algebra of the formula shows another answer as demonstrated. If you don’t 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’t the interpretation of the probability distribution be subject to the formula calculation ?
Awaiting your reflection and suggestion. Thankyou.
March 30, 2021 at 4:17 pm
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.
April 8, 2021 at 9:48 am
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 ?
April 8, 2021 at 4:12 pm
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.
September 16, 2021 at 1:03 am
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
January 22, 2021 at 4:09 pm
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. 🙂
January 23, 2021 at 9:32 am
Thank you for your comment 🙂
December 3, 2020 at 11:14 am
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).
December 3, 2020 at 3:28 pm
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).
December 26, 2019 at 8:40 pm
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)?
December 27, 2019 at 7:34 am
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.
September 6, 2019 at 9:56 am
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 ?
September 6, 2019 at 9:07 am
Hi SIr, Can you please explain again what you meant by area of bar is proportional to frequency. I cant seem to understand it
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