Question

Please help so I can explain to my daughter what to do...
the lipton tea company pack tea in bags marked as 250 g. A large number of packs of tea were weighed and the mean and standard deviation were calculated at 255 g and 2.5 g respectively. Assuming this data is normally distributed, what percentage of packs are underweight?

Answer 1

what does "underweight " mean? below 255?

Answer 2

I'm assuming so

Answer 3

oh now sorry, probably below 250 as stated on the pack

Answer 4

ah ok

Answer 5

you need to find how many standard deviations below the mean 250 is
then use some kind of table

Answer 6

Ok I'm not sure how to do that... 9th grade was a long time ago. I'm studying for my exam and trying to figure out how to help her haha

Answer 7

the standard deviation is 2.5 and \(5\div 2.5=2\) so 5 below 255, namely 250 is 2 standard deviations below the mean

Answer 8

this is not how the math teachers say it, they say "convert to z score" etc, but it amounts to the same thing
then you have to look at a table and see what percent of normally distributed data is less than two standard deviations below the mean
since 2 is a nice whole number, some people actually know this by heart, but i do not

Answer 9

You lost me... I don't understand how to see what it is below the mean?

Answer 10

And what table?

Answer 11

you have to have a table for normally distributed data
if you do not have one in a text, you can find one on line
i can back up and go slower if that would help

Answer 12

It may.. let me ask her if she has a table

Answer 13

here is a picture of the normal distribution

Answer 14

oh my gosh

Answer 15

I think I'm going to have an aneurysm trying to figure this out.

Answer 16

you can see from the label in the picture that \(95.6\%\) of the data lie within two standard deviations of the mean
btw trust me, this is not that bad, i know no statistics at all, just bear with it

Answer 17

ok lie, 95.4% of the data lie withing two standard deviations of the mean

Answer 18

Ok..

Answer 19

do you understand how that is labelled in the picture?

Answer 20

Yes because its 2 out each way

Answer 21

right,
now the normal distribution is symmetric which is a fance way of saying it is the same left and right of the mean.
so if 95.4% lie within two standard deviation from the mean, \[100\%-95.4\%=4.6\%\] lie outside of that range

Answer 22

half above two standard deviations, half below
you only want the half that is below, so half of \(4.6\%\) is \(4.3\%\) and you are done, except for the understanding maybe of where we got the two standard deviations from

Answer 23

typo

Answer 24

i meant half of \(4.6\%\) is \(2.3\%\) sorry

Answer 25

So the answer is 2.3% of packages are underweight

Answer 26

Ok I think I understand this to explain it to her lol **Fingers crossed**

Answer 27

yes
we didn';t even need a table for this because the z score was a nice whole number

Answer 28

Oh wait in the beginning you did 5 divided by 2.5... is that 5 just the difference between 255 and 250?

Answer 29

we can go over again how we found the 2 standard deviations below
the mean is 255, you want 550 or below \[255-250=5\] divide that by the standard deviation get \[5\div2.5=2\]

Answer 30

yes that is where the 5 came from

Answer 31

Oh okay... I'm going to try and relay this to her now. Thank you so much

Answer 32

yw, and good luck!