Math Probability: Need to find the Variance

[CryptoMath]

Homework Statement

Weight of the plums of a large lot is averaging 70 g and SD 0.85 g.
X= the average weight of plums in a pack of 14 plums.

Find the variance of the variable X.

Homework Equations

The Attempt at a Solution

n=14
Average_Total= 70*14=980
SD² = Variance_Total= 0.85² *12 = 10.115

Variance/n = 10.115/14 =0.7225

Does that make sense so far? I am pretty much stuck here.

 

[andrewkirk]

You'll find it easier to understand if you write sentences around your formulas, explaining what they represent.
For instance, what is 'Average_Total' and why did you write

Variance/n

I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.

Writing explanatory sentences helps it fit together in a logical manner in your mind, rather than just being a jumbled bunch of formulas that you try to commit to memory, hoping to use the right one at the right time.

 

[CryptoMath]

You'll find it easier to understand if you write sentences around your formulas, explaining what they represent.
For instance, what is 'Average_Total' and why did you write

I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.

Writing explanatory sentences helps it fit together in a logical manner in your mind, rather than just being a jumbled bunch of formulas that you try to commit to memory, hoping to use the right one at the right time.

Average_Total: as in the average of all the 14 plums.

Variance/n : To have the average variance I believe as this is what its asking in the problem
X= the average weight of plums in a pack of 14 plums.
and I need to find the variance.

But what distribution do I have to follow, is this binomial ?

 

[CryptoMath]

You'll find it easier to understand if you write sentences around your formulas, explaining what they represent.
For instance, what is 'Average_Total' and why did you write

I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.

Writing explanatory sentences helps it fit together in a logical manner in your mind, rather than just being a jumbled bunch of formulas that you try to commit to memory, hoping to use the right one at the right time.

I got this one resolved it is simply that:
Variance/n = 0.85²/14 =0.060208, this is the answer.
Checked in my book to confirm :)

 

[andrewkirk]

That's right, the formula that the variance of a sum of independent random variables is the sum of the variances is true regardless of distribution.
BTW, the problem statement omitted to say that the weight of plums in the pack is independent, which is essential to obtaining the solution. In practice, that may not be the case, depending on how the sample of 14 was selected. For instance if there is a lot of jostling there will be more larger plums near the top, and smaller near the bottom. So 14 plums selected from near one another would be expected to have correlated sizes.

 

[CryptoMath]

That's right, the formula that the variance of a sum of independent random variables is the sum of the variances is true regardless of distribution.
BTW, the problem statement omitted to say that the weight of plums in the pack is independent, which is essential to obtaining the solution. In practice, that may not be the case, depending on how the sample of 14 was selected. For instance if there is a lot of jostling there will be more larger plums near the top, and smaller near the bottom. So 14 plums selected from near one another would be expected to have correlated sizes.

I have an other exercise, may you help me with that one please ?

 

[andrewkirk]

OK. Post it as a new thread though, unless it's very closely related, to avoid confusing readers..

 

[CryptoMath]

OK. Post it as a new thread though, unless it's very closely related, to avoid confusing readers..

https://www.physicsforums.com/threads/math-probability-need-to-find-the-variance.857348/