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.

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.

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????

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.

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 )

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.

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

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

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).

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.

vuongquan says

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.

4mula says

please how did you get the z as 1.645

John Moffat says

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.

jb29 says

i thought the z score answer in the normal distribution table represents the area lying to the left of the given X value

John Moffat says

It is to the left or to the right because the curve is symmetrical.

MuhammedSaleem says

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????

John Moffat says

Yes, but it doesn’t matter if it is positive or negative because the curve is symmetrical. Therefore the sign does not matter.

MuhammedSaleem says

ok thank u sir

John Moffat says

You are welcome 馃檪

annsh901 says

Hey John, in example 2, shouldn鈥檛 the 50% of 10 cms be 5, or am I doing something wrong?

John Moffat says

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.

sohaib.ahmad says

sir in the exam. if the answer is fill in the blanks. should we write it as a percentage or decimal?

John Moffat says

It will be made clear which is required 馃檪

Morgan137 says

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?

John Moffat says

Yes. The curve is symmetrical about the mean and so the proportion more (or less) than the mean is always 50%.

Nyasha27 says

Thank you sir for the lecture. Why doesn’t this chapter and the last chapter have practice questions?

Nyasha27 says

This is new to me and I would love to exercise it a bit more please

John Moffat says

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 )

sabya2k says

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 ?

John Moffat says

Yes we would 馃檪

Abhsn says

In what cases do we subtract the probability from 0.5?

John Moffat says

When we are looking for the probability of being above or below a certain value (as I show in my free lectures).

Asif110 says

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

John Moffat says

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.

Asif110 says

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.

John Moffat says

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.

sejazkhan says

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

?

John Moffat says

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.

Lamini says

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

Univer@2024 says

Where is 1.645 coming from?

FinKi says

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

John Moffat says

Thank you for your comment 馃檪

ABDULLAHI312 says

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).

John Moffat says

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).

faizalcs says

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)?

John Moffat says

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.

iza1 says

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 ?

iza1 says

Hi SIr,

Can you please explain again what you meant by area of bar is proportional to frequency.

I cant seem to understand it