# probability of normal variable

#### shawnteh1711

##### New Member
What are the chances that X̄ > µ?

A. ¼

B. ½

C. ¾

D. 1

Please advise I thought that probability of X̄ greater than µ should be depended on confidence level and p-value. For example, taking 95% confidence level, there is 2.5% that the X̄ greater than µ,

#### obh

##### Active Member
Hi Shawnteh,

You have it in the wrong way ...
The definition of accumulate distribution is p(X≤x)
p(X>x)=1-p(X≤x)

Now if you know the population's standard deviation, you can calculate the average's standard deviation,
And the mean of the average is the mean of the population.

The confidence interval is a range that the random variable will be in a probability of the confidence level.
For example, if the confidence level is 0.95, the probability that the random variable will be in the confidence range is 0.95.

#### obh

##### Active Member
Hi Shawnteh,

You have it in the wrong way ...
The definition of accumulate distribution is p(X≤x)
p(X>x)=1-p(X≤x)

Now if you know the population's standard deviation, you can calculate the average's standard deviation,
And the mean of the average is the mean of the population.

The confidence interval is a range that the random variable will be in a probability of the confidence level.
For example, if the confidence level is 0.95, the probability that the random variable will be in the confidence range is 0.95.
Or did you miss some input data...?

#### Dason

Or did you miss some input data...?
I doubt it. This sounds like a standard homework question

#### obh

##### Active Member
Hi Dason Clearly, this is homework, but I think we didn't get the entire question #### Dason

Hi Dason Clearly, this is homework, but I think we didn't get the entire question I'm making the assumption that at some point the question/prompt says it's normally distributed (because of the title of the thread...) which provides enough info to answer the question.

#### obh

##### Active Member
Yes, of course , I just imagined a more complex question like "what is the probability that X̄ is greate than the right range confidence interval ...

So Shawneth, just look on a normal chart and tell us, what is the probability that a normally distributed variable will be greater than the mean? (as the mean of the average is also the mean of the population ...)

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#### shawnteh1711

##### New Member
Yes, of course , I just imagined a more complex question like "what is the probability that X̄ is greate than the right range confidence interval ...

So Shawneth, just look on a normal chart and tell us, what is the probability that a normally distributed variable will be greater than the mean? (as the mean of the average is also the mean of the population ...)
50%