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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
John Moffat says
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.
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.
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
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
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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