# 02 -Normal Distribution

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02 -Normal Distribution

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