Thread: S.D.

Can anyone help me with this question??

The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

i) taller than 189cm
ii)taller than 179cm
iii)between 174cm and 199cm
iv) over 199cm tall?

thank you

How far have you gone in your calculations or understanding of the problem?

Given a normal distribution, there are certain percentages that correspond to certain standard deviations. I'm sure you can find these percentages online, and once you have them, the answers to your questions should be very easy to obtain.

Originally Posted by Heinsbergrelatz

Can anyone help me with this question??

The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

i) taller than 189cm
ii)taller than 179cm
iii)between 174cm and 199cm
iv) over 199cm tall?

thank you

As Alexp said, if the distribution is normal your questions can be answered using a table for the normal distribution.. It is not possible to calculate the answers exactly but the necessary integral has been approximated numerically and the results tabulated -- which is what the table for the normal distribution really is.

On the other hand this question, with no further qualification, demonstrates a fundamental lack of understanding of probability theory on the part of whoever formulated the question. Unless you know the form of the distribution there is no a priori relationship between the standard deviation and probabilities. Moreover, I can guarantee that the height of basketball players is not exactly normally distributed -- if it were there would eventually be a basketball player of negative height.

height is typically normally distributed, maybe its not exactly normally distributed but it is a good approximation.

Originally Posted by organic god

height is typically normally distributed, maybe its not exactly normally distributed but it is a good approximation.

How good the approximation is depends entirely on your purpose.

I can guarantee that the height is not precisely normally distributed.

yes, you can guarantee this,

However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

Therefore for a theoretical basketball population, a normal distribution is the best one available

Originally Posted by organic god

yes, you can guarantee this,

However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

Therefore for a theoretical basketball population, a normal distribution is the best one available

One more time. That depends entirely on your application.

There is zero justification for your statement.

The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.

Originally Posted by Heinsbergrelatz

Can anyone help me with this question??

The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

i) taller than 189cm
ii)taller than 179cm
iii)between 174cm and 199cm
iv) over 199cm tall?

thank you

Just answer "Ir is impossible to say" for all three.

You might not get any marks for ir but you will be right!!

Originally Posted by DrRocket

Originally Posted by organic god

yes, you can guarantee this,

However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

Therefore for a theoretical basketball population, a normal distribution is the best one available

One more time. That depends entirely on your application.

There is zero justification for your statement.

The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.

One more time

In this situation, the probability distribution is not known, the question is used to test the students understanding of the normal distribution.

I don't see why this is upsetting you so much

Originally Posted by organic god

Originally Posted by DrRocket

Originally Posted by organic god

yes, you can guarantee this,

However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

Therefore for a theoretical basketball population, a normal distribution is the best one available

One more time. That depends entirely on your application.

There is zero justification for your statement.

The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.

One more time

In this situation, the probability distribution is not known, the question is used to test the students understanding of the normal distribution.

I don't see why this is upsetting you so much

I am not upset at all. Read my posts more carefully.

I have simply pointed out the unstated and not necessarily true assumptions that have been made by whoever wrote the question.

I understand what the questioner intended the sudent to do. I also understand why that is an exercise in blindly applying a formula that may or may not be appropriate, depending on what one is really trying to do.

Probability theory is deeper than many statisticians appreciate.

Recognizing that the probability distribution is not known is the starting point for recognizing the potential errors in applying formulas by rote.