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Edexcel statistics 2 - number of games needed in stock

There's been debate over this question that was on the edexcel statistics 2 exam paper yesterday.

3. An online shop sells a computer game at an average of rate of 1 per day.
(a) Find the probability that the shop sells more than 10 games in a 7 day period. (3 marks)
This wasn't the debated part
X~Po(7)
P(X>10) = 1 - P(X=<10) = 1 - 0.9015 = 0.0985

Once every 7 days the shop has games delivered before it opens.
(b) Find the least number of games the shop should have in stock immediately after a delivery so that the probability of running out of the game before the next delivery is less than 0.05. (3 marks)
For this part, there's a confusion over whether it's 12 or 13.
I thought it was 13 because:
P(X>11) = 1 - P(X=<11) = 1 - 0.9467 = 0.0533
P(X>12) = 1 - P(X=<12) = 1 - 0.9730 = 0.0270
.: Need at least 13 games in stock to not run out of the game.

If anybody could explain what the correct answer should be for part b, I'd really appreciate it. :smile:

Reply 1

ghostwalker

Original post by k1rby

I thought it was 13 because:
P(X>11) = 1 - P(X=<11) = 1 - 0.9467 = 0.0533
P(X>12) = 1 - P(X=<12) = 1 - 0.9730 = 0.0270
.: Need at least 13 games in stock to not run out of the game.

If anybody could explain what the correct answer should be for part b, I'd really appreciate it. :smile:

It's 13, IMHO.

If you have 12 games in stock, then you will runout if 12 people purchase the game, which they do with probability 1-P(X<=11)= 0.0533. Which is greater than 0.05.

Reply 2

cooldudeman

I got 13 too because they used the word 'least' which in the past similar questions did not.

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Reply 3

ljh950912

..

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Reply 4

Revengeissweet

It would be good to get some opinions from teachers

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Reply 5

Jakub675

Basically the book shows that when it says run out u use p(x>n). Which is how u get 12 games. On the s2 chat I posted 3 examples from the book that support 12

Reply 6

Jakub675

The word least has nothing to do with working this put. And anyway there is an example in the book that has the word least in it and uses a method that gives the answer 12

Reply 7

milliezhao

The edexcel text book supports 12, they have to mark 12 right otherwise it will damage their reputation for being inconsistent. Personally i think both answers are correct depends on how one interpret "out of stock".

Reply 8

ghostwalker

Original post by milliezhao

"Out of stock" has only one meaning that I am aware of, and that is you have no more stock; not you have a customer whom you can't supply.

If Edexcel choose to interpret it differently, then IMAO, they are wrong.

Reply 9

Robbie242

This is good news, so only sampling has hurt me if edexcel aren't wrong that is

Reply 10

Hamburglar

On the mark scheme it has to be either 13, or 13 and 12.

As far as I know the answer has to be 13. I'll post my toilet roll analogy here because why not:

Say you've just taken a fresh dump, and there are 10 squares of toilet paper left. You manage to wipe your ass successfully with exactly 10 squares and you're happy. The demand has been met. However, surely you've also ran out of TP. Just because the demand has been met doesn't mean you didn't actually run out. I used 10 squares, and therefore I had 0 left at a given point in time, regardless of whether anyone else needed a dump that day or not.

If the answer to this question is 12, then you are saying that after using the 10 sheets of TP, you didn't run out of toilet roll because the demand has been met. Except you have ran out of toilet roll though because there's none left, regardless of whether anyone ever uses that toilet ever again. Your dump could have been an absolute monstrosity which destroyed the toilet and nobody will ever use it again, does this mean you never run out of toilet paper because there is no more demand?

HOWEVER - some questions I've seen agree with the "12" method, but in my opinion they are wrong because of the above logic.

To conclude: Edexcel should either accept 13 or both answers. 13 because it is right, and both answers because the text book teaches it that way.

Sorry if I seem a bit "I'm right go away" but I've had to try an explain this a lot today. xD Everything above is just an opinion and if you disagree, please let me know why.

EDIT: Also, definition of "run out": become used up; be exhausted; "Our supplies finally ran out".

Something runs out when it is used up and in other words, when the quantity falls to zero.

(edited 10 years ago)

Reply 11

Jakub675

This argument can go on forever. Logic supports the answer being 13 but the edexcel book, official book of the board that makes these exams supports 12. So instead of sitting here and saying the same things over and over again, we should just forget about it focus on our other exams and wait till the official mark scheme comes out

Reply 12

cooldudeman

Original post by Hamburglar

Bravo!

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Reply 13

Akshay.M

Original post by k1rby

P(X>11) = 1 - P(X=<11) = 1 - 0.9467 = 0.0533
P(X>12) = 1 - P(X=<12) = 1 - 0.9730 = 0.0270
.: Need at least 13 games in stock to not run out of the game.

To use N=13 You must write P(X>=13) = 1 - P(X=<12) = 1 - 0.9730 = 0.0270
To use N=12 You must write P(X>12) = 1 - P(X=<12) = 1 - 0.9730 = 0.0270

If you used the wrong justification for the answer I doubt you'd get the marks.

If you think of it like this:
Poisson has a constant rate of 7 per week, so if you say your demand per week in this question is 12 (which we all agree), then we consider your argument for 13 games, you'll have 1 extra game in stock before each new delivery. So as the weeks go on the numbers of left-over games you have will increase by 1 each week. Clearly this suggests the answer is not the minimum stock.

However if you stock 12 games you meet demand exactly and the issue of building up stock doesn't occur, thus this shows the stores minimum stock is 12.