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#1 2011-07-23 22:42:35

nevinsmith
Member
Registered: 2010-05-19
Posts: 39

probability question binormal distribution

A small restaurant seats 20 diners and is full every night. There are only 12 steaks available and 40% of diner tables will request a steak, indepedent of each other.
one table can only order one steak.

If a customer orders a steak, what is the probability that he/she will recieve it?

Any tips? I can't seem to get the answer which is actually 0.996315 to 6sf

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#2 2011-07-23 22:59:43

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: probability question binormal distribution

hi nevinsmith

welcome to the forum.

just one question:is the demand of the steak always 40%?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2011-07-23 23:11:44

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: probability question binormal distribution

Hi nevinsmith,

Is there more information?

Will there be 12 steaks every night? How many diners per table?
40% tables will order a steak means, even if there are 20 tables only 8 steaks will be ordered and everyone gets one!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#4 2011-07-23 23:15:15

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: probability question binormal distribution

hi gAr

exactly my thoughts.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2011-07-23 23:20:18

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: probability question binormal distribution

Hi anonimnystefy,

Okay.
How are doing with calculus? How is it going?

Last edited by gAr (2011-07-23 23:20:46)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#6 2011-07-23 23:38:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

Hi nevinsmith;

I would have to say have you copied the problem correctly?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2011-07-24 00:00:34

nevinsmith
Member
Registered: 2010-05-19
Posts: 39

Re: probability question binormal distribution

basically, there is a probability of 40% that any table will order steak everynight. only 12 steaks are available at any one night. Given that someone orders strak, what is the probability that he will recieve a steak (they haven't ran out)

I think i actually solved the problem lol but it's just the aweful rounding.

anyway calculus is going good. thanks guys!

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#8 2011-07-24 00:10:42

nevinsmith
Member
Registered: 2010-05-19
Posts: 39

Re: probability question binormal distribution

to Gar '40% tables will order a steak means, even if there are 20 tables only 8 steaks will be ordered and everyone gets one!'

thats not quite true, not 40% of tables, each table has 40% chance of wanting to order one.
so there is a probability that all tables will want to order one

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#9 2011-07-24 00:17:04

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: probability question binormal distribution

Hi nevinsmith,

I'm still unable to understand the question.
Have you copied the question verbatim?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#10 2011-07-24 00:18:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

I am sorry, I am having trouble with it too.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2011-07-24 00:23:17

nevinsmith
Member
Registered: 2010-05-19
Posts: 39

Re: probability question binormal distribution

alright, this is the question word by word

A small restaurant seats 20 diners, and is full everynight. The chef knows from previous
experience that 40% of diners order steak. So she always has 12 in her fridge at beginning
of each night.
a customer can only order one steak maximum.

If a customer orders steak, what is the probability that he/she will recieve one?

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#12 2011-07-24 00:40:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

Hi nevinsmith;

I am getting an answer of .99078


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2011-07-24 00:52:36

nevinsmith
Member
Registered: 2010-05-19
Posts: 39

Re: probability question binormal distribution

hi bobbym,

How did you do it?

I took the sums of probability of more than 12 people (12,13,14...19) multiplied by the probability that the specific person won't get one of the 12 steaks (1/13, 2/14, 3/15 etc)
then 1-Ans
comes pretty close to the actual answer

Is there a shorter way? The exam allocates 40min for binormal distribution and there is no way i can answer this one in less than 10min lol

thanks for the help so far

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#14 2011-07-24 00:55:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

I did it using a standard normal curve but I do not know if that is right?

What is your answer?

I am not happy with my answer. This a discrete problem and my solution is a continuous one. It might be close but I doubt it is right.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2011-07-24 05:12:23

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,354

Re: probability question binormal distribution

hi nevinsmith, bobbym and gAr

The chef knows from previous experience that 40% of diners order steak.

I'm interpreting this as

"The chef knows from previous experience that there is a probability that a diner will order steak of 40%."

That makes it a standard binomial problem with n = 20 and p = 0.4 (q = 0.6)

So I have computed P(x=13) + P(x=14) + .... + P(x=20)  (see picture of Excel calculations)

That comes to 0.978971072522229....

Perhaps I should also do a normal approximation. 

mean = 8 sd = 2.19089  P(x>12.5) = 0.9798  P(x>13) = 0.9887

Now that's the probability that not all steak ordering customers are satisfied.  12 of them will be.

So maybe I've got to do

P(orders = 13) and then P(of being the one customer who doesn't get one)
P(orders = 14) and then P(of being one of the two who don't get one)
...................................................................................................
P(orders = 20) and then P(of being one of the 8 customers who don't get one)

That's going to take a bit longer.


Bob

View Image: Nevinsmith.GIF

Last edited by bob bundy (2011-07-24 05:25:13)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#16 2011-07-24 05:22:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

Hi bob bundy;

Good afternoon to you. I got bluffed off of that answer by ...

I can't seem to get the answer which is actually 0.996315 to 6sf


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#17 2011-07-24 05:26:59

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,354

Re: probability question binormal distribution

Good day to you bobbym

I've just added a further edit to that post.

revised calculation gives 0.997846

The 'customer' column is calculated with the formula P(X) * (X-12)/X

eg P(15) = 0.001294 then multiply by 3/15 as three out of fifteen will be unlucky.

I think that's my best stab at it.

Bob

View Image: Nevinsmith2.GIF

Last edited by bob bundy (2011-07-24 05:36:21)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#18 2011-07-24 05:50:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability question binormal distribution

Hi bob;

It is close, maybe his is a typo.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#19 2011-07-24 07:34:18

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,354

Re: probability question binormal distribution

Hi bobbym,

Well maybe.  But it's a odd one.  I've thought of maybe a rounding difference but cannot get to his digits.  All is based on a re-interpretation of the question.  Just wait and see I suppose.

bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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