02 -Normal Distribution

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02 -Normal Distribution by Mind Map: 02 -Normal Distribution

1. Tips

1.1. Direct Excel or via Z, based on the unknown

1.1.1. Excel

1.1.1.1. P

1.1.1.2. X

1.1.2. via Z

1.1.2.1. σ

1.1.2.2. μ/x

2. So What

2.1. f (x)

2.1.1. Determining the probability of things happening

2.1.1.1. profits

2.1.1.2. quality thresholds

2.1.1.3. defect rates

3. Z Score

3.1. Formula

3.1.1. Z=(X - μ)/σ

3.1.2. σ=(X - μ)/Z

3.1.3. X=Zσ+μ

3.1.4. μ= (X -Zσ)

3.2. What?

3.2.1. # of σ from μ

3.2.2. Z~N(0,1) {Z norm. distri with...)

3.2.3. value

3.2.3.1. + => above μ

3.2.3.2. - => below μ

3.3. So What

3.3.1. typicality of a value in the set

4. CLT

4.1. What

4.1.1. Layman's : average of sample is normal with its population given n>=30

4.1.2. Approximation becomes accurate with n increasing. I.e. gets close to the population size

4.2. So What

4.2.1. converts any distribution to normal distribution?

4.2.1.1. Application

4.2.1.1.1. Hypothesis testing

4.2.1.1.2. Confidence levels of unknown μ

4.2.1.2. Because, averaging is smoothing out extremes

4.2.2. I.e. ability to infer population parameters based on the sample results

4.3. Assumptions

4.3.1. population variance(σ2) is finite

4.3.1.1. whats the big deal

4.4. Insights

4.4.1. distribution of the sample mean is centred at the population mean despite the sample size

4.4.1.1. why?

4.4.2. distribution of the sample MEAN becomes normal with sample size n increases

4.4.3. As n increases variability of sample mean decreases

5. Standard Error

5.1. What

5.1.1. sd(x-BAR)=σ/√n

5.1.1.1. why √n?

5.1.2. standard deviation of the sampling distribution

5.2. So what