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Can someone help me with Statistics 2?

Hello,

Can someone check this for me, please?

In a coffee shop one in four customers asks for biscuits with coffee. Use normal distribution approximations to calculate:

1. The probability to 4 d.p., that for the first 100 customers fewer than 20 will ask for biscuits with their coffee.

My answer is 0.102, is it correct?

Thank you!

ImageUploadedByStudent Room1427134434.969814.jpg
sorry if it looks a bit dodgy :biggrin:




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Original post by minime_w
Hello,

Can someone check this for me, please?

In a coffee shop one in four customers asks for biscuits with coffee. Use normal distribution approximations to calculate:

1. The probability to 4 d.p., that for the first 100 customers fewer than 20 will ask for biscuits with their coffee.

My answer is 0.102, is it correct?

Thank you!

ImageUploadedByStudent Room1427134434.969814.jpg
sorry if it looks a bit dodgy :biggrin:




Posted from TSR Mobile


Your method is correct if it were a binomial distribution being approximated but I suspect that it is the other distribution, (one in four) being the giveaway for a rate.
Reply 2
Original post by SeanFM
Your method is correct if it were a binomial distribution being approximated but I suspect that it is the other distribution, (one in four) being the giveaway for a rate.


Hi,

Thank you for replying!

How would you do it?


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Original post by minime_w
Hi,

Thank you for replying!

How would you do it?


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I would use the Poisson distribution first instead of the Binomial.
Reply 4
Original post by SeanFM
I would use the Poisson distribution first instead of the Binomial.


How would it look like with Poisson distribution? Y~P(_)?

What about the 100 customers?


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Original post by minime_w
How would it look like with Poisson distribution? Y~P(_)?

What about the 100 customers?


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What is the rate for 4 customers?

Then what is the rate for 100 customers?
Reply 6
Original post by SeanFM
What is the rate for 4 customers?

Then what is the rate for 100 customers?


1/4 x 100/4?

don't get it :frown:


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Original post by minime_w
1/4 x 100/4?

don't get it :frown:


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Hmm, not quite. To put it another way, if it's 1 in 4, how many is it in 100?
Reply 8
Original post by SeanFM
Hmm, not quite. To put it another way, if it's 1 in 4, how many is it in 100?


Po(25)? :/


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Bingooo :smile: well done.

Now can you do the rest of the question?
Reply 10
Original post by SeanFM
Bingooo :smile: well done.

Now can you do the rest of the question?


Yes :smile: well the first part...

Can you help me with this one as well?:frown:

The smallest value of n such that there is a probability of at least 0.98, that fewer than n of the 100 customers will ask for biscuits.

Do I just find the smallest value that is greater than 0.98 on the tables?
Like 0.9803=2.06

Thank you!!!
Original post by minime_w
Yes :smile: well the first part...

Can you help me with this one as well?:frown:

The smallest value of n such that there is a probability of at least 0.98, that fewer than n of the 100 customers will ask for biscuits.

Do I just find the smallest value that is greater than 0.98 on the tables?
Like 0.9803=2.06

Thank you!!!


At least 0.98, so yes. How can you find n from that z value?
Reply 12
Original post by SeanFM
At least 0.98, so yes. How can you find n from that z value?


I don't know? It said 2.06 next to 0.9803, I was hoping that was all that I needed to do .. lol
Original post by minime_w
I don't know? It said 2.06 next to 0.9803, I was hoping that was all that I needed to do .. lol


Okey dokey.

So you know what your value of z needs to be. If P(y<n) = p(Z<2.06), what is n?
(edited 9 years ago)
Reply 14
Original post by SeanFM
Okey dokey.

So you know what your value of z needs to be. If P(y<n) = p(Z<2.06), what is n?



i don't know :frown:
Original post by minime_w
i don't know :frown:


In your example, although it was binomial, you went from n=19.5 to z = -1.27.

So in the same way, but for Poisson, your n would match up to give z=2.06. Do you see why? If so, can you find n?
Reply 16
Original post by SeanFM
In your example, although it was binomial, you went from n=19.5 to z = -1.27.

So in the same way, but for Poisson, your n would match up to give z=2.06. Do you see why? If so, can you find n?



I still don't get it :frown:

I used P(Z < x - μ / σ)

no sign of n :frown:
Original post by minime_w
I still don't get it :frown:

I used P(Z < x - μ / σ)

no sign of n :frown:


Your n is the x value - you just need to figure out what the x is.
Reply 18
Original post by SeanFM
Your n is the x value - you just need to figure out what the x is.


ohh, but how do I work out x?
Original post by minime_w
ohh, but how do I work out x?


P(X<x) = P(Z < x - μ / σ)

Your z value, which is x - μ / σ, is equal to 2.06. As you know μ and σ, how do you find x?

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