Calculate the mean for a normal distribution

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SUMMARY

The discussion clarifies that the mean (μ) and standard deviation (σ) of a normal distribution are independent parameters. Specifically, with a standard deviation of 500, the mean can take on any value, such as -500, 0, or even 5.723×101091. This independence means that knowing one does not provide information about the other, which is a fundamental concept in statistics.

PREREQUISITES
  • Understanding of normal distribution properties
  • Knowledge of statistical terms: mean (μ) and standard deviation (σ)
  • Familiarity with basic statistical equations
  • Concept of independence in statistical parameters
NEXT STEPS
  • Study the properties of normal distributions in depth
  • Learn about the implications of parameter independence in statistics
  • Explore how to calculate other statistical measures related to normal distributions
  • Investigate applications of normal distributions in real-world scenarios
USEFUL FOR

Students studying statistics, educators teaching statistical concepts, and professionals working with data analysis who need to understand the relationship between mean and standard deviation in normal distributions.

ptlnguyen
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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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