Stats question

A firm of caterers wishes to buy wine for a wedding reception of 200 guests. They estimate that, on average, each guest will drink 45 cl of wine. The volume of wine in the bottles they buy may be assumed to have a distribution with mean 70.5 cl and standard deviation 1.2 cl. Show that if they buy 128 bottles then the caterers can be more than 95% certain that their requirements can be met.

Please answer!!

Reply 1

RDKGames

Study Forum Helper

[QUOTE=sharryborgan;66451844]A firm of caterers wishes to buy wine for a wedding reception of 200 guests. They estimate that, on average, each guest will drink 45 cl of wine. The volume of wine in the bottles they buy may be assumed to have a distribution with mean 70.5 cl and standard deviation 1.2 cl. Show that if they buy 128 bottles then the caterers can be more than 95% certain that their requirements can be met.

Please answer!!

I'm assuming distribution is normal. In which case I'm unsure whether the question is wrong or I am because my z value is too negative...

Reply 2

Ayman!

Not sure if the way I did it is correct, but...

Spoiler

Reply 3

asinghj

Here's how I did it, assuming it was a normal distribution.
z = (x - 70.5)/1.2
P(Z<z) = 0.95, therefore P(Z>z) = 0.05
From tables, z = 1.6449
Rearranged the equation above, x = 72.47
There are 128 bottles, so 72.47 * 128 = 9276.16
There were 200 guests, each want 45cl,
so 200 * 45 = 9000
9000 / 9276.16 * 100 = 97.02
97.02% > 95%
QED

Reply 4

Zacken

Original post by sharryborgan

Please answer!!

Er, no. This isn't a "do-my-work-for-me-pls!" site, please add your own thoughts and attempts to the question before we nudge you along the right path.

Reply 5

sharryborgan

Original post by Ayman!

Not sure if the way I did it is correct, but...

Spoiler

Thanks that's much appreciated

Reply 6

sharryborgan

Original post by asinghj

Thanks a lot

Reply 7

username1162972

Original post by Zacken

Er, no. This isn't a "do-my-work-for-me-pls!" site, please add your own thoughts and attempts to the question before we nudge you along the right path.

You dnt even knw the answer anyway. Dumbo.
This is propa maths

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Reply 8

sharryborgan

Original post by physicsmaths

You dnt even knw the answer anyway. Dumbo.
This is propa maths

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At least I do write proper English, as for being a dumbo, I do have a PhD.

Reply 9

username1162972

Original post by sharryborgan

At least I do write proper English, as for being a dumbo, I do have a PhD.

Well I wasn't talking to you. But now that you have tried to assert your better then me, your struggling on easy maths and I wrote like that on purpose because well, this is the internet and I know Zacken so it was a joke. Get a grip on your life with your PhD, how is that working out for you?

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Reply 10

sharryborgan

Original post by physicsmaths

I thought you were talking to me. I do not assert that I am better than anyone, My PhD is in Quantum Physics and I do not have much knowledge about stats, hence my question. Let's put this all down to a misunderstanding.

Reply 11

17lina

I have a question as well from S2!
When using the poission distribution and I end up with a parameter that does not end with 0.5 or an integer such as 3.75, do I round it up to 4 or is it the average?? 😭😭