# Normal distribution

Watch this threadPage 1 of 1

Go to first unread

Skip to page:

Deannnn97

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#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]

PLEASE HELP

(a) What is the standard deviation of this distribution? [3 marks]

(b) What is the probability of a value greater than 60? [2 marks]

PLEASE HELP

0

reply

gdunne42

Badges:
21

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2

Report

#2

(Original post by

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]

PLEASE HELP

**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]

PLEASE HELP

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.

Posted from TSR Mobile

0

reply

RDKGames

Badges:
20

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3

Report

#3

**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]

PLEASE HELP

(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

0

reply

Deannnn97

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4

thanks man helps so much, just the grey areas in the diagram, how do you get this from the 2.5%?

0

reply

RDKGames

Badges:
20

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5

Report

#5

(Original post by

thanks man helps so much, just the grey areas in the diagram, how do you get this from the 2.5%?

**Deannnn97**)thanks man helps so much, just the grey areas in the diagram, how do you get this from the 2.5%?

0

reply

Deannnn97

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6

(Original post by

Do you mean the corresponding z value from 2.5%? Just refer to the normal distribution data table for that.

**RDKGames**)Do you mean the corresponding z value from 2.5%? Just refer to the normal distribution data table for that.

0

reply

RDKGames

Badges:
20

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7

Report

#7

(Original post by

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?

**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?

0

reply

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#8

(Original post by

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.

**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.

b) would be 0.975%?

0

reply

Badges:
20

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#9

Report

#9

0

reply

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#10

(Original post by

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.

**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

reply

Badges:
20

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#11

Report

#11

(Original post by

So what are the answers?

**Deannnn97**)So what are the answers?

0

reply

X

Page 1 of 1

Go to first unread

Skip to page:

### Quick Reply

Back

to top

to top