# Normal distribution

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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

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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#2

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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#3

(Original post by

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

**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

I feels a bit like you're going through the motions without understanding properly what you're doing.

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#4

**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

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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(Original post by

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.

**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.

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(Original post by

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?

**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?

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#7

(Original post by

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?

**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?

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.

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

If I stated: ,

does that remind you of anything?

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(Original post by

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: ,

does that remind you of anything?

**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: ,

does that remind you of anything?

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so 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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#10

(Original post by

so 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?

**Yazomi**)so 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?

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:

Say you desire: .

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

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

Does this make sense?

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For this question, we do not need to standardise.

So here, do you agree:

is given by: ?

Last edited by simon0; 4 months ago

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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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#12

(Original post by

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

**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

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.

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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Ahaaa this makes more sense now, thank you so much for helping!! 😁

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(Original post by

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.

Figure on right is the Standard Normal Distribution (image from: https://www.mathsisfun.com/data/imag...ndardizing.svg ).

**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.

Figure on right is the Standard Normal Distribution (image from: https://www.mathsisfun.com/data/imag...ndardizing.svg ).

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#15

(Original post by

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?

**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?

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#19

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 () 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.

For your question, the probability of obtaining a sample mean of 21.2 or greater () 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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