Yazomi
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Z~N(0,1^2)
Find p(-2.30<Z<0)
Why is the answer 0.4893 and not -0.4893,
I got 0.5-0.9893
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username3331778
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draw a normal curve and shade the region you are interested in then think about the symmetry; and what value the tables in the formula book are giving you
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Sir Cumference
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(Original post by Yazomi)
Z~N(0,1^2)
Find p(-2.30<Z<0)
Why is the answer 0.4893 and not -0.4893,
I got 0.5-0.9893
It doesn't make sense for probability to be negative...

I feels a bit like you're going through the motions without understanding properly what you're doing.
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simon0
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(Original post by Yazomi)
Z~N(0,1^2)
Find p(-2.30<Z<0)
Why is the answer 0.4893 and not -0.4893,
I got 0.5-0.9893
Probabilities can only take on values between and including 0 and 1.

You need to find the area underneath the Standard Normal Distribution curve and the x-axis between -2.3 and 0.

Are you aware of how to do this?
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Yazomi
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(Original post by Sir Cumference)
It doesn't make sense for probability to be negative...

I feels a bit like you're going through the motions without understanding properly what you're doing.
I’m currently having to self teaching myself these following chapters coz ya know coronavirus but yeah I find this topic difficult to understand. I’ve done practice questions which helps with my understanding but there are some of the times where I have no idea why I’m doing it but the theory fits if that makes sense
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Yazomi
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(Original post by simon0)
Probabilities can only take on values between and including 0 and 1.

You need to find the area underneath the Standard Normal Distribution curve and the x-axis between -2.3 and 0.

Are you aware of how to do this?
I realise what went wrong now thanks tho I’m currently not too sure about the link between standardising normal distribution? I see you need to use the equation z=(x-mean)/(sigma) but I don’t see why other to get the answer right? Does standard normal distribution is the same as all the other distribution?
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simon0
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(Original post by Yazomi)
I realise what went wrong now thanks tho I’m currently not too sure about the link between standardising normal distribution? I see you need to use the equation z=(x-mean)/(sigma) but I don’t see why other to get the answer right? Does standard normal distribution is the same as all the other distribution?
The Standard Normal Distribution is the Normal Distribution with mean 0 and standard deviation 1 and seen as a "standard".

If you use tables to find probabilities, the table refers to this Normal Distribution and the z formula ((x - mean)/sd) is used to convert from/to other Normal distributions with different mean and standard deviation.

-----------------------------------------------------------------------------------------------------

So here, we do not need to use the z formula (as we are already working with the Standard Normal Distribution).

If I stated:  P ( a \leq Z \leq b ) = P (Z \leq b) - P (Z \leq a) ,

does that remind you of anything?
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Yazomi
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(Original post by simon0)
The Standard Normal Distribution is the Normal Distribution with mean 0 and standard deviation 1 and seen as a "standard".

If you use tables to find probabilities, the table refers to this Normal Distribution and the z formula ((x - mean)/sd) is used to convert from/to other Normal distributions with different mean and standard deviation.

-----------------------------------------------------------------------------------------------------

So here, we do not need to use the z formula (as we are already working with the Standard Normal Distribution).

If I stated:  P ( a \leq Z \leq b ) = P (Z \leq b) - P (Z \leq a) ,

does that remind you of anything?
Ahh yes I remember the mean of 0 and SD 1 but not what you’ve stated, I’m currently only in y12 but doing the y2 stats, what’s the point of using the table if it doesn’t give you enough possible values and you could use the calculator to get the probability?
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Yazomi
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Name:  292ABCE5-E095-4A7E-B69C-EA5283A2C799.jpg.jpeg
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Size:  62.9 KBso this is the notes we’ve got given but we’re currently on half term so I can’t really ask my teachers rn but for the example, are 0.10565 and 0.77337 the probability value for the z value or? The thing I’m confused about for the moment is how does the standard normal distribution fits for all the other random variable. Like are all the curves the same but just have different mean and sd value?
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simon0
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(Original post by Yazomi)
Name:  292ABCE5-E095-4A7E-B69C-EA5283A2C799.jpg.jpeg
Views: 11
Size:  62.9 KBso this is the notes we’ve got given but we’re currently on half term so I can’t really ask my teachers rn but for the example, are 0.10565 and 0.77337 the probability value for the z value or? The thing I’m confused about for the moment is how does the standard normal distribution fits for all the other random variable. Like are all the curves the same but just have different mean and sd value?
Your last sentence is (mostly) true.
Normal Distribution curves with different means and standard deviations can be shifted and rescaled to the Standard Normal Distribution (with mean 0 and standard deviation 1) using the "z-formula".

Using the example used in your notes, let:

 X \sim N(50, 4^{2} ) .

Say you desire:  P ( 50 \leq X \leq 55) .

Then usually, you need to convert the limits x=50 and x=55 to the standardised z values (using the z formula) so:

  P ( 50 \leq X \leq 53) = P ( 0 \leq Z \leq 1.25 ) = \Phi (1.25) - \Phi (0).

(Today, the new UK A-level specification demands you use a calculator to find probabilities using the Normal Distribution).

Does this make sense?

-----------------------------------------------------------------------

For this question, we do not need to standardise.
So here, do you agree:

 P( -2.3 \leq Z \leq 0 ) is given by:  \Phi (0) - \Phi (-2.3) ?
Last edited by simon0; 4 months ago
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Yazomi
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I got the same answer to the first one and the second question I agree with it as well but how do you know when you need to standardise or unstandardise or would the question say so
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simon0
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(Original post by Yazomi)
I got the same answer to the first one and the second question I agree with it as well but how do you know when you need to standardise or unstandardise or would the question say so
When you have been asked to find probabilities of the Normal Distribution with mean 0 AND standard deviation 1, there is no need to standardise as this is the Standard Normal Distribution (you can use the z formula to convert the limit value a, say, however you just end up with the same value i.e. Z = (a-0)/1 = a).

If you are dealing with Normal Distributions with different mean and different standard deviation, then you need to standardise the x-value limits. Then you can use tables to look up the probability values.

Image

Figure on right is the Standard Normal Distribution (image from: https://www.mathsisfun.com/data/imag...ndardizing.svg ).
Last edited by simon0; 4 months ago
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Yazomi
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Ahaaa this makes more sense now, thank you so much for helping!! 😁
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Yazomi
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(Original post by simon0)
When you have been asked to find probabilities of the Normal Distribution with mean 0 AND standard deviation 1, there is no need to standardise as this is the Standard Normal Distribution (you can use the z formula to convert the limit value a, say, however you just end up with the same value i.e. Z = (a-0)/1 = a).

If you are dealing with Normal Distributions with different mean and different standard deviation, then you need to standardise the x-value limits. Then you can use tables to look up the probability values.

Image

Figure on right is the Standard Normal Distribution (image from: https://www.mathsisfun.com/data/imag...ndardizing.svg ).
Do you mind if I just ask for one for question😅 Name:  6660FE17-F9CA-4612-BA77-B4CBCC823AD0.jpg.jpeg
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Size:  19.0 KBhow would you know which sign to use for two tailed test (</>) to find the probability and wouldn’t this be reject H0 instead because the statistical value lied in the critical region of you draw the diagram?
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RDKGames
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(Original post by Yazomi)
Do you mind if I just ask for one for question😅 how would you know which sign to use for two tailed test (</>) to find the probability and wouldn’t this be reject H0 instead because the statistical value lied in the critical region of you draw the diagram?
Side comment: get out of the habit of saying "Accept H_0"
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Yazomi
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(Original post by RDKGames)
Side comment: get out of the habit of saying "Accept H_0"
What should I say instead?🤔
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RDKGames
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(Original post by Yazomi)
What should I say instead?🤔
Do not reject H_0.
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Yazomi
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(Original post by RDKGames)
Do not reject H_0.
Ahaa I see, do you know the answers to the question I posted by any chance as well
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simon0
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You are mixing up probabilities with the z values (the value 0.2755 is the probability, not the z-value).

For your question, the probability of obtaining a sample mean of 21.2 or greater ( P( \bar{X} \geq 21.2) ) is 0.2755 which is greater than 0.025.
So no need to reject the null hypothesis as it is still more likely than 2.5% to obtain a sample mean of 21.2 or greater.
Last edited by simon0; 4 months ago
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