Normal Distribution Mastery Guide

Flashcards about the Normal Distribution

What is the normal distribution also known as?

Gaussian distribution

What are the key characteristics of a normal distribution?

Symmetry, Mean=Median=Mode, Bell-Shaped Curve, Asymptotic, Defined by two parameters

What is the normal distribution also known as?

Gaussian distribution

What are the key characteristics of a normal distribution?

Symmetry, Mean=Median=Mode, Bell-Shaped Curve, Asymptotic, Defined by two parameters

What does the Empirical Rule state about data spread in a normal distribution?

68% within 1 standard deviation, 95% within 2 standard deviations, 99.7% within 3 standard deviations

What is the formula for the probability density function (PDF) of a normal distribution?

f(x)=12πσ2 e−(x−μ)22σ2

What are the parameters in the normal distribution formula?

μ (mean) and σ (standard deviation)

What are the characteristics of a standard normal distribution?

μ=0 and σ=1

How do you convert a normal distribution to a standard normal distribution?

Use the z-score formula: z=x−μσ

What does a z-score indicate?

How many standard deviations an element is from the mean

What do percentiles represent?

The percentage of data below a certain point

How does adding or subtracting a constant affect a normal distribution?

Shifts the mean (μ) but doesn't affect the standard deviation (σ)

How does multiplying or dividing by a constant affect a normal distribution?

Scales both the mean and standard deviation by that constant

What does the area under the normal distribution curve represent?

Probabilities of a value falling within that range

What does the Central Limit Theorem (CLT) state?

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases

Give some practical applications of Normal Distribution.

Quality Control, Standardized Testing, Natural Phenomena, Finance