Chapter 6: The Normal Distribution

The Central Limit Theorem

: sample size n, mean µ, and standard deviation σ are given.

Calculator function for probability

: normalcdf (lower x value of the area, upper x value of the area, mean, standard deviation)

Standard normal distribution

: a normal distribution with a mean of µ= 0 and a standard deviation of σ= 1.

Normal Distribution

: X- N (µ, σ) where µ is the mean and σ is the standard deviation.

normal distribution curve

A(n) is unimodal.

Normal distribution

A bell curve or a Gaussian distribution curve

Approximately normally distributed variables

Many continuous variables (e.g

Standard normal distribution

a normal distribution with a mean of µ = 0 and a standard deviation of σ = 1

Z-score formula

𝑿 − 𝝁 / σ

(P → X)

𝑿 = 𝝁 + 𝝈Z

Calculator function for probability

normalcdf (lower x value of the area, upper x value of the area, mean, standard deviation)

Calculator function for the kth percentile

k = invNorm (area to the left of k, mean, standard deviation)

Sampling distribution of sample means

a distribution using the means computed from all possible random samples of a specific size taken from a population

Sampling error

the difference between the sample measure and the corresponding population measure because the sample is not a perfect representation of the population

The Central Limit Theorem

sample size n, mean µ, and standard deviation σ are given

Standard error of the sample mean

𝝈/ √𝑛

Properties of the Theoretical Normal Distribution

Mean = Median = Mode

A normal distribution curve is unimodal.

The curve never touches the x-axis.

The total area under a normal distribution curve is equal to 1.00

Number of units (individual/items) satisfying a condition

→ Total number of units given in the problem × are calculated based on condition