Calculate the mean for a normal distribution

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The mean (μ) of a normal distribution cannot be calculated solely from the standard deviation (σ), as they are independent parameters. A standard deviation of 500 allows for any value of the mean, meaning μ can be any number, including negative or extremely large values. This independence highlights that knowledge of one does not determine the other. Therefore, without additional information, the mean cannot be derived from the standard deviation alone. Understanding this relationship is crucial for correctly interpreting normal distributions.
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Homework Statement



Given:
Standard Deviation = 500

Homework Equations



How I calculate the μ (mean) using standard deviation for a norma distribution. Thanks.

The Attempt at a Solution

 
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ptlnguyen said:

Homework Statement



Given:
Standard Deviation = 500

Homework Equations



How I calculate the μ (mean) using standard deviation for a norma distribution. Thanks.

The Attempt at a Solution


Short answer: you can't.

Longer answer: the mean μ and standard deviation σ are independent, so you can have σ = 500 but μ = -500, μ = 0, μ= 5.723×1091 or any other value you want.
 

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