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.

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.

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. 🙂

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.

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’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.

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.

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. 🙂

John Moffat says

Thank you for your comment 🙂

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