Stats Chapter 7 Topic Test guides

Features/ Charcateristics of a normal distribution

Symetric bell shaped curve

Parameter of a normal distribution

mean (𝜇) and standard deviation (𝜎)

Role of the parameter of the normal probability distribution

determines the location and shape of the distribution 

Role of 𝜇

determines the location of the center, a change can cause the graph to shift left or right

Role of (σ

determines the shape of of the distribution, a change can cause the shape of the curve to become fatter or skinner

Emperical rule

68% of data within 1 SD, 95% within 2 SD, and 99.7% within 3 SD

Limitations of empirical rule

Only applies to data that is approximately normally distributed

Interpretation: Standard normal distribution/ Z distribution/ Z score

z score measure how many SD the data is from the mean

Finding the probability when the z-score is given.

normalcdf(lower limit, upper limit, mean, SD)

Finding z-score when probability is given

Inversenormal(Area to the left, mean, SD)

Equation: Standard normal distribution/ Z distribution/ Z score

z= X−μ​/ 𝜎)

Area under any normal curve

find X (not standardized) when given by converting it to Z use normalcdf

Finding the x when the probability is given

find Z using inverse normal then concert it to X

Relationship between sampling distribution and population distributtion

sampling distribution (μₓ̄) = population mean (μ), standard deviation of the sampling distribution (σₓ̄) =σ/√n

What is standard error SE?

the standard deviation of a sampling distribution, measures how much the sample mean varies from the population mean 

Equation for SE

σ/√n

Use of normalcdf

finds the probability (area) under the curve between X or Z

Use of invnormal

Finds the value of X or Z