A statistical question confusing for beginners! "The Coffee shop's mean sales are $2000 a day, with a standard deviation of $1000..."

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metinerol

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Hi to everybody! I am new here and new in statistics. I have recently done a quiz and my answer is different than the answer given. Below is the original question:

"The Coffee shop's mean sales are $2000 a day, with a standard deviation of $1000. what're the probabilities of sales will be between $2000 to $ 4000. Provide the answer in percentages and one decimal place."

Basically I thought that mean value (2,000) is in the middle of the values. Besides when z=-+2, then it covers 95%, which is between 0 and 4000. I thought between 0 and 2000 should be 50%, because coffee shop cannot sell negative value, so the least number it sells must be "0". The data after 4,000 should cover the other 5%. As after 2000 is 50%, and after 4000 is 5%, I thought between 2000-4000, it should be 45% (50-5)....However it seems wrong. Can somebody explain why I am wrong? I ams ure mathematically I am correct, but is there sth different with the statistics?

Thank you in advance!

Metin
 
metinerol said:
Hi to everybody! I am new here and new in statistics. I have recently done a quiz and my answer is different than the answer given. Below is the original question:

"The Coffee shop's mean sales are $2000 a day, with a standard deviation of $1000. what're the probabilities of sales will be between $2000 to $ 4000. Provide the answer in percentages and one decimal place."

Basically I thought that mean value (2,000) is in the middle of the values. Besides when z=-+2, then it covers 95%, which is between 0 and 4000. I thought between 0 and 2000 should be 50%, because coffee shop cannot sell negative value, so the least number it sells must be "0". The data after 4,000 should cover the other 5%. As after 2000 is 50%, and after 4000 is 5%, I thought between 2000-4000, it should be 45% (50-5)....However it seems wrong. Can somebody explain why I am wrong? I ams ure mathematically I am correct, but is there sth different with the statistics?

Thank you in advance!

Metin
Click to expand...
Why do you think it's wrong? Did someone say you are, or does it just not feel right?

Your thinking, though a little long and convoluted, is good. (It suggests that you haven't learned much about this yet, but are doing well with what you know.)

But there is one error. If the data between -2 and +2 standard deviations is about 95%, then the remaining 5% covers both values above z=2 and below z=-2. As you note, in reality there can't be values below 0; but the normal distribution doesn't know that! If the data were really normally distributed, then half of the 5% would be negative; and since you've been told to assume it's normal, you need to pretend those negative values are possible.

(What's really happening is that the data can't be exactly normal! You've discovered a flaw in the problem -- which is probably very common in courses at this level!)

So, what percentage is between z=0 and z=2, in a normal distribution, ignoring the facts of the problem?
 
metinerol said:
"The Coffee shop's mean sales are $2000 a day, with a standard deviation of $1000. what're the probabilities of sales will be between $2000 to $ 4000. Provide the answer in percentages and one decimal place."
Click to expand...
What is the distribution of the random variable representing daily sales? The normal distribution would have non-zero probability of negative values, which makes no sense.
 
blamocur said:
What is the distribution of the random variable representing daily sales? The normal distribution would have non-zero probability of negative values, which makes no sense.
Click to expand...
I hadn't even noticed that it didn't explicitly say (as many problems do) to assume (an approximately) normal distribution.

I imagine this problem was given at a point ("new in statistics") where students are expected to make that assumption. Very likely the topic being taught is the "empirical rule", which implicitly or explicitly assumes it.

Under this assumption, @metinerol is very wise to have seen the contradiction.

But a textbook should tell you when they want you to do so, and should mention that it is not always a good assumption!
 
Dr.Peterson said:
Why do you think it's wrong? Did someone say you are, or does it just not feel right?

Your thinking, though a little long and convoluted, is good. (It suggests that you haven't learned much about this yet, but are doing well with what you know.)

But there is one error. If the data between -2 and +2 standard deviations is about 95%, then the remaining 5% covers both values above z=2 and below z=-2. As you note, in reality there can't be values below 0; but the normal distribution doesn't know that! If the data were really normally distributed, then half of the 5% would be negative; and since you've been told to assume it's normal, you need to pretend those negative values are possible.

(What's really happening is that the data can't be exactly normal! You've discovered a flaw in the problem -- which is probably very common in courses at this level!)

So, what percentage is between z=0 and z=2, in a normal distribution, ignoring the facts of the problem?
Click to expand...
Thank you Peterson, I also believe this is the case: " (What's really happening is that the data can't be exactly normal! You've discovered a flaw in the problem -- which is probably very common in courses at this level!).

I really don't care about if I did it correctly or not. I just want to learn how it should be really done. I got it now after reading all responses here. Thank you all! and yes..., the question asked us to assume it is a normal distribution.
 
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