Re: Normal Distribution Probability problem. Please help!

minimus wrote:

I see onyl one sample and one mean of that sample.
Use your imagination. Imagine more.

No need to imagine anything. Lets just discuss the facts of statistics.

Ok, let us do that. It might be interesting.

Why mean itself has a distribution?
Because the mean in this problem is a sum of heights divided by N. And those heights ARE random variables. Expected value has no sense in (b).

Heights are random variables. But heights can be random variables in one single population.

Agreed. And I still can't see how you can compute the mean in the question other than the arithmetic mean of those random variables.

>>> Why mean itself has a distribution?

Let me try one more time. The answer is : because the mean is a function of those random variables. Is it better now? We are still talking about this exam question. If not, please start another thread (here or in sci.stat.edu) and we can discuss the general setting, group (or "sample") and the mean, and should we treat it or not as a random variable.

For something to be a random variable, we dont need a value to be drawn from samples.

I didn't say that, did I?

Ok, since this is sci.stat.math I think we now need to agree about some definition of a random variable. No, I do not mean "a function on some measurable space". Some sensible description so we are sure that we are talking about the same basic concept.

If I have one population (hence one sample - ok sample in this case is abused but that does nto change the fact)
then I still have a random variable and that random variable has a distribution.

You mean a collection of random variables (each person's height being one of them), right? Or this time I am missing something ?

Why do we assume that there are many subsamples and each has a mean, and hence the mean has a distribution...?
Primary reason - to answer the question and get marks.

I think we cannot get anywhere with this logic. no ofenses.

None taken.

[..]

We are assuming that this group is a sample from some population(s) of boys' and girls' heights. We are doing it purely hypothetically. We assume this because we DON'T KNOW what has been (or will be) observed, and want to give an answer to the question "find the probability that ...". It is just a model, this model is stated right at the beginning of the question. We are not assuming any subsamples from this year-group but that this year group can be thought of as a sample from some larger, hypothetical population.

This is clear. But we need a reason to assume that there are samples and not one sample (which is then the population).

Ok, lets forget about populations and samples. We have a set of heights, unknown, about to be measured.

Why mean is a random variable?
Because we do not know its value? And because we are assuming some magic mechanism producing heights, this mechanism is summarized by two numbers (parameters of normal distribution).

What do you mean?

I'm afraid I can't write it any simpler.

>We can jsut compute the mean given the values. And
that is the mean of that population.

What values? Do you mean the parameters of those distributions? Because we are still talking about this simple exam question. And "we can just compute the mean". But mean of what ? There are no data to compute from. All we have is a collection of random variables, nothing has been measured yet, it is unknown and there different possible results we could get, with different probabilities (assuming the probabilistic model stated). Or you are suggesting to treat "mean" here as the expected value?

JoJO

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