Dear Pit,

I have a maths test tomorrow on probability, and I was wondering if anyone here could help me understand Inverse Normal Problems using bell-curves. I understand Normal Problems, all I have to do is find the upper and lower values, and we are told the standard deviation and mean so that is not a problem, but I suck at the Inverse's. Instead of finding a probability, with the Inverse Normal Problems you've got to find the value of a percentage. So you have to find the area, standard deviation and mean. I have no idea how to do these, I can't find the values of a probability I can only find the probability.

Here's an example of a question I'm trying to answer:

"Find the random variable 'x' for the normal distribution (mean= 63.4 and standard deviation= 15.6)"

P(X>x) = 0.2177"

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To somewhere safer
where the feeling stays.
I want to love you but
I'm getting blown away.
Isn't it just 1-what the value on the normal distribution table is?

My stats is a bit rusty, but as i remember, first you wuld standardize the mean and SD, and then find the value of 1-0.2177 on the table, then find out how that P relates to your mean and SD. Like, the value with P(1-0.2177) would be mean+(SD.y) and that would be x.

Yea?
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Isn't it just 1-what the value on the normal distribution table is?

My stats is a bit rusty, but as i remember, first you wuld standardize the mean and SD, and then find the value of 1-0.2177 on the table, then find out how that P relates to your mean and SD. Like, the value with P(1-0.2177) would be mean+(SD.y) and that would be x.

Yea?

Thanks for the quick response.

How do I standardize the mean and SD? Sorry if that's a stupid question, but I'm really confused.

You are like a hurricane
And I'm gettin' blown away
To somewhere safer
where the feeling stays.
I want to love you but
I'm getting blown away.
Bump.

Sorry if there are rules against bumping or w/e, but I really need to know this.
You are like a hurricane
And I'm gettin' blown away
To somewhere safer
where the feeling stays.
I want to love you but
I'm getting blown away.
Quote by estranged_g_n_r
Thanks for the quick response.

How do I standardize the mean and SD? Sorry if that's a stupid question, but I'm really confused.

Ok i just re-read your first question and by 'Normal Problems' do you mean the normal distribution? If yes, then to standardize a x value you have to perform a Z-transformation: Z = (X-mean)/SD

So if you had a normal distribution but didn't know that values on a table, you would standardize the X data value then read the probability off the standard normal distribution table which almost all exams give you.

The trick with your question is that you aren't told the X data value, so you have to work backwards.

Okay, so you know what a normal curve looks like yea? And in the Q it asks for a value that has a probability of 0.2177 above that value. So, logically that value has 1-0.2177 = 0.7823 P below it.

So, your standardized value Z has to equal something with a standard normal probability of 0.7823. Look at the table, it's 0.78.

So, (X-mean)/SD has to equal 0.78.
Plug in the numbers, X = 75.568

Yea?
Quote by bassplayer33333
Sinisa Rules all.

Quote by zbest
That is part of the reason that the mafia does so much drug trafficing, its so they wont die of hunger because they dont have anything.
Quote by sinisa
Ok i just re-read your first question and by 'Normal Problems' do you mean the normal distribution? If yes, then to standardize a x value you have to perform a Z-transformation: Z = (X-mean)/SD

Oops, yeah sorry, I meant Normal Distribution. So by the Z-transformation, you're saying that I divide the mean by the SD and then what?

So if you had a normal distribution but didn't know that values on a table, you would standardize the X data value then read the probability off the standard normal distribution table which almost all exams give you.

The trick with your question is that you aren't told the X data value, so you have to work backwards.

Okay, so you know what a normal curve looks like yea? And in the Q it asks for a value that has a probability of 0.2177 above that value. So, logically that value has 1-0.2177 = 0.7823 P below it.

So, your standardized value Z has to equal something with a standard normal probability of 0.7823. Look at the table, it's 0.78.

So, (X-mean)/SD has to equal 0.78.
Plug in the numbers, X = 75.568

Yea?

Yeah, that's the right answer, I just don't get that part about the Z-transformation. Thanks for the help so far, you're a lifesaver.
You are like a hurricane
And I'm gettin' blown away
To somewhere safer
where the feeling stays.
I want to love you but
I'm getting blown away.
Quote by estranged_g_n_r
Oops, yeah sorry, I meant Normal Distribution. So by the Z-transformation, you're saying that I divide the mean by the SD and then what?

Yeah, that's the right answer, I just don't get that part about the Z-transformation. Thanks for the help so far, you're a lifesaver.

Ach should have made that clearer. Take the X data value, subtract the mean, divide by SD. Z = (X - [mean])/SD

The big trick in that question was working backwards. Usually they'll be like, what is the probability of X>x given mean = 325 and SD = 24. But in this case it was a matter of working back from the table.

But seriously, you should have already learnt all of this quite thoroughly if you have a test on it tomorrow? Slackness on your part to practice methinks

Anyway, no problem
Quote by bassplayer33333
Sinisa Rules all.

Quote by zbest
That is part of the reason that the mafia does so much drug trafficing, its so they wont die of hunger because they dont have anything.
Quote by sinisa
Ach should have made that clearer. Take the X data value, subtract the mean, divide by SD. Z = (X - [mean])/SD

The big trick in that question was working backwards. Usually they'll be like, what is the probability of X>x given mean = 325 and SD = 24. But in this case it was a matter of working back from the table.

But seriously, you should have already learnt all of this quite thoroughly if you have a test on it tomorrow? Slackness on your part to practice methinks

Anyway, no problem

Ok thanks. Yeah, a bit of slackness, but also I don't really need to know these things, the teacher said it's very unlikely that these questions will come up, but I decided to learn them just in case.