You are Here: Home >< Maths

# Stats help? Standard distribution question

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. So I've got this question on my homework:

Packets of currants are nominally 500g in weight. The actual weights may be modelled by a Normal distribution with mean 508.3g and standard deviation 4.8g. What is the probability that a packet is underweight?
If an adjustment can be made to the machine which alters the mean but leaves the standard deviation unchanged, what should be the new mean weight if less than ½% of the packets are to be underweight?

I've done the first half & got 0.0419 as the probability (assuming that underweight means less than 500g). But for the second part I'm not sure what ½% means? I've never seen a fraction and a percentage put together so I'm not sure whether to take it as 0.5% or 50% (and then the probability is 0.5)?
2. look at the small table and 1/2 = 0.5 right? so look for 0.5 and place the value there

then place it into the formula
(Original post by ltbitters)
So I've got this question on my homework:

Packets of currants are nominally 500g in weight. The actual weights may be modelled by a Normal distribution with mean 508.3g and standard deviation 4.8g. What is the probability that a packet is underweight?
If an adjustment can be made to the machine which alters the mean but leaves the standard deviation unchanged, what should be the new mean weight if less than ½% of the packets are to be underweight?

I've done the first half & got 0.0419 as the probability (assuming that underweight means less than 500g). But for the second part I'm not sure what ½% means? I've never seen a fraction and a percentage put together so I'm not sure whether to take it as 0.5% or 50% (and then the probability is 0.5)?
3. (Original post by ltbitters)
So I've got this question on my homework:

Packets of currants are nominally 500g in weight. The actual weights may be modelled by a Normal distribution with mean 508.3g and standard deviation 4.8g. What is the probability that a packet is underweight?
If an adjustment can be made to the machine which alters the mean but leaves the standard deviation unchanged, what should be the new mean weight if less than ½% of the packets are to be underweight?

I've done the first half & got 0.0419 as the probability (assuming that underweight means less than 500g). But for the second part I'm not sure what ½% means? I've never seen a fraction and a percentage put together so I'm not sure whether to take it as 0.5% or 50% (and then the probability is 0.5)?

Think about it this way. 50% is half, so 0.5.

5% is 10 times less.

0.5% is 10 times less.

and 1/2 = 0.5. It is a bit strange to see it like that but I think that's how you should interpret it, by converting the franction into a number and not forgetting the %.
4. this is different this is standard distribution, he's wondering what is the value of 0.5 and to find the value of this you go on the small table
(Original post by SeanFM)
Think about it this way. 50% is half, so 0.5.

5% is 10 times less.

0.5% is 10 times less.

and 1/2 = 0.5. It is a bit strange to see it like that but I think that's how you should interpret it, by converting the franction into a number and not forgetting the %.
5. (Original post by zainyyyyy)
this is different this is standard distribution, he's wondering what is the value of 0.5 and to find the value of this you go on the small table
Did you even read the question? No and don't phrase it wrong just because the title phrased it differently. This is Normal distribution, it even says so in the question context. And the OP is wandering what value to use, not what he needs to do.
6. (Original post by zainyyyyy)
this is different this is standard distribution, he's wondering what is the value of 0.5 and to find the value of this you go on the small table
I believe the question is asking primarily about what (1/2)% means, just like when you say the value for which 50% of values of the distribution is less than it is the mean, or in this case the value for which 0.5% (a very small number) is less than the 'underweight' boundary.

Though you do indeed go to the small table
Spoiler:
Show
to find 0.005 or 0.995 or whichever one it is, depending on what the table looks like.
(Original post by SeanFM)
I believe the question is asking primarily about what (1/2)% means, just like when you say the value for which 50% of values of the distribution is less than it is the mean, or in this case the value for which 0.5% (a very small number) is less than the 'underweight' boundary.

Though you do indeed go to the small table
Spoiler:
Show
to find 0.005 or 0.995 or whichever one it is, depending on what the table looks like.
8. (Original post by RDKGames)
Did you even read the question? No and don't phrase it wrong just because the title phrased it differently. This is Normal distribution, it even says so in the question context. And the OP is wandering what value to use, not what he needs to do.
ahhh yeah sorry for the confusion!! its normal distribution lol ive just started stats so im still a little confused about names and stuff D:
9. (Original post by SeanFM)
I believe the question is asking primarily about what (1/2)% means, just like when you say the value for which 50% of values of the distribution is less than it is the mean, or in this case the value for which 0.5% (a very small number) is less than the 'underweight' boundary.

Though you do indeed go to the small table
Spoiler:
Show
to find 0.005 or 0.995 or whichever one it is, depending on what the table looks like.
although i have absolutely no idea what the small table is (just started S2 this week & ive never done S1 so it might be an S1 thing i just dont know about? idk) this helped a lot so thank you!!
10. (Original post by ltbitters)
although i have absolutely no idea what the small table is (just started S2 this week & ive never done S1 so it might be an S1 thing i just dont know about? idk) this helped a lot so thank you!!
Check the back of your textbook or your formula booklet (if you're with Edexcel, it's in both of those places) and the S1 tables should hopefully be in the S2 textbook. The small table, also known as percentage points or something, gives you different 'special' values for when you can't read them off the 2 d.p tables. 1/2 % is an example of that, 1/10 % might be on there as well. Just in case you get a question with a low (or high, if you're looking at the other end.. you can apply the usual logic to go from P(Z<z) = 0.001 to P(Z greater than or equal to z) = 0.999. and find the answer.
11. (Original post by SeanFM)
Check the back of your textbook or your formula booklet (if you're with Edexcel, it's in both of those places) and the S1 tables should hopefully be in the S2 textbook. The small table, also known as percentage points or something, gives you different 'special' values for when you can't read them off the 2 d.p tables. 1/2 % is an example of that, 1/10 % might be on there as well. Just in case you get a question with a low (or high, if you're looking at the other end.. you can apply the usual logic to go from P(Z<z) = 0.001 to P(Z greater than or equal to z) = 0.999. and find the answer.
oohhh :00 i always wondered why there were tables of numbers in the formula book lol

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: September 11, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams