# Problem with averages and standard deviation.

#### nickar1172

##### New member
I had this problem on a quiz and obviously got it wrong, I am confused about how to set this question up and what to solve for:

In a large city, the average retail price of a pound of grapes is $1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16 of all pounds of butter sold in this city? I posted this question in another forum and somebody told me that it was unsolvable but obviously it can be if I got it wrong.... #### MarkFL ##### Administrator Staff member I have moved this thread to our Basic Probability and Statistics subforum as it is a better fit. The question gives information about grapes, and then asks about butter. Perhaps this is why you were told is it unanswerable. Assuming we are talking about the same product, are you told anything about the distribution of the data? Are they normally distributed? #### chisigma ##### Well-known member I had this problem on a quiz and obviously got it wrong, I am confused about how to set this question up and what to solve for: In a large city, the average retail price of a pound of grapes is$1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16 of all pounds of butter sold in this city?

I posted this question in another forum and somebody told me that it was unsolvable but obviously it can be if I got it wrong....
Of course the problem is solvable if you have some type of information abut the p.d.f. of the r.v. ... for example if the price [that we call P...] is uniformely distributed from a to b the its mean value is $\mu = \frac{a + b}{2}$ and the standard deviation is $\sigma = \frac{b-a}{\sqrt{12}}$ and You can esasily find a and b...

Kind regards

$\chi$ $\sigma$

#### nickar1172

##### New member
it was a typo its supposed to be grapes and grapes, still looking for help please

#### MarkFL

Staff member
it was a typo its supposed to be grapes and grapes, still looking for help please
Have you been given any information regarding distribution of the data?

#### nickar1172

##### New member
Have you been given any information regarding distribution of the data?
No this was all I was given, what type of distribution is also needed because there is an a) part which stated: using the computing formula, find the standard deviatin of the sample:

2, 6, 4, 7, 3, 1

#### MarkFL

Staff member
No this was all I was given, what type of distribution is also needed because there is an a) part which stated: using the computing formula, find the standard deviatin of the sample:

2, 6, 4, 7, 3, 1
The formulas for sample standard deviation $s$ are:

$$\displaystyle s=\sqrt{\frac{\sum\left(x-\overline{x} \right)^2}{n-1}}$$

$$\displaystyle s=\sqrt{\frac{n\left(\sum x^2 \right)-\left(\sum x \right)^2}{n(n-1)}}$$

Can you proceed?

#### nickar1172

##### New member
I got the standard deviation for that question but what does that have to do with the original question that I posted about the grapes???

#### MarkFL

Staff member
I got the standard deviation for that question but what does that have to do with the original question that I posted about the grapes???
I don't see that the two are related.

#### nickar1172

##### New member
exactly my point taken HOW do you solve the original question.....

#### nickar1172

##### New member
Does anyone know how to solve this???

In a large city, the average retail price of a pound of grapes is $1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16 of all pounds of grapes sold in this city? #### MarkFL ##### Administrator Staff member Does anyone know how to solve this??? In a large city, the average retail price of a pound of grapes is$1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16 of all pounds of grapes sold in this city?
I might be wrong (stats is not a strong area for me), but I really think you need information regarding the distribution of the data.

#### Jameson

The only way I could see answering this problem would be to assume that $\dfrac{15}{16}$ of the area of a normal curve for price is connected to that amount of sales, but that's a stretch. It's a weird problem and I feel (like others) that something is off.
In a large city, the average retail price of a pound of grapes is $1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16 of all pounds of grapes sold in this city? The question can be answered if You get some hypothesis on the p.d.f. of the price P. It must be P>0, so that a normal distribution probably isn't appropriate. In... http://mathhelpboards.com/basic-pro...erages-standard-deviation-8093.html#post37192 ... the case of uniform distribution between a and b is considered and in that case is$\displaystyle \mu= \frac{b + a}{2}$and$\displaystyle \sigma= \frac{b - a}{\sqrt{12}}$. The data You have permit fo find a and b solving the linear system...$\displaystyle b + a = 3.58\displaystyle b - a = .18\ \sqrt{12}\ (1)$... and You obtain a = 1.48 and b = 2.1. The$\frac{15}{16}$of prices lie in the interval 1.5 < P < 2.08 ... Kind regards$\chi\sigma\$