# Normal distribution

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#1
A Normal distribution has a mean of 50, and the proportion of the distribution less than 40 is 2.5 %.
(a) What is the standard deviation of this distribution? [3 marks]
(b) What is the probability of a value greater than 60? [2 marks]

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5 years ago
#2
(Original post by Deannnn97)
A Normal distribution has a mean of 50, and the proportion of the distribution less than 40 is 2.5 %.
(a) What is the standard deviation of this distribution? [3 marks]
(b) What is the probability of a value greater than 60? [2 marks]

A. There are ways to calculate this exactly but I assume you are being asked this question to test understanding of the basic normal distribution curve. Approximately 95% of data lies within 2 standard deviations above and below the mean. B. the curve is symmetrical about the mean.

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5 years ago
#3
(Original post by Deannnn97)
A Normal distribution has a mean of 50, and the proportion of the distribution less than 40 is 2.5 %.
(a) What is the standard deviation of this distribution? [3 marks]
(b) What is the probability of a value greater than 60? [2 marks]

In the case you need to work these out:

(a) Lay out the information first; ~ Therefore: Next you are told that the probability that the proportion of the distribution less than 40 is 2.5% thus: which looks like:

and due to symmetry around the mean;

Which means that:   From here we need to convert out probability into the z value by means of the normal distribution table; and now we can sub it into our formula for z and solve for ; which is the standard deviation.

(b) We found it in part (a) as part of out working out
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#4
thanks man helps so much, just the grey areas in the diagram, how do you get this from the 2.5%?
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5 years ago
#5
(Original post by Deannnn97)
thanks man helps so much, just the grey areas in the diagram, how do you get this from the 2.5%?
Do you mean the corresponding z value from 2.5%? Just refer to the normal distribution data table for that.
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#6
(Original post by RDKGames)
Do you mean the corresponding z value from 2.5%? Just refer to the normal distribution data table for that.
No i mean the grey area, from 40 down and 60 up, how does this represent 2.5%? I get 40 as this is part of the question, and so you copy this onto the otherside making it 60, but where how does the 2.5% effect it, for example if the question was; the proprtion of distribution less than 40 is 1%, how would this differ?
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5 years ago
#7
(Original post by Deannnn97)
No i mean the grey area, from 40 down and 60 up, how does this represent 2.5%? I get 40 as this is part of the question, and so you copy this onto the otherside making it 60, but where how does the 2.5% effect it, for example if the question was; the proprtion of distribution less than 40 is 1%, how would this differ?
Well the question outlines this percentage for us, saying less than 40 is 2.5% so that's what I represented on the graph; everything less than 40 is 2.5%. If you were to change only the percentage, you would be altering the standard deviation.
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#8
(Original post by RDKGames)
Well the question outlines this percentage for us, saying less than 40 is 2.5% so that's what I represented on the graph; everything less than 40 is 2.5%. If you were to change only the percentage, you would be altering the standard deviation.
ok so a) would be 1.96
b) would be 0.975%?
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5 years ago
#9
(Original post by Deannnn97)
ok so a) would be 1.96
b) would be 0.975%?
No and no.The z value is not the standard deviation. Probability it's more than 60 is the same as probability its less than 40.
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#10
(Original post by RDKGames)
No and no.The z value is not the standard deviation. Probability it's more than 60 is the same as probability its less than 40.
0
5 years ago
#11
(Original post by Deannnn97)
Well I'm not here to solve your questions for you. Think. I literally did most of the working out for you in (a) and answered b as part of working out in (a).
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