The Normal Distribution

Question 1

The Normal Distribution

Answer 1

An ideal, symmetric, and unimodal distribution that many empirical observations look similar to

Question 2

The Mean(μ) & Standard Deviation (σ)

Answer 2

μ: middle of the bell
σ: describes how spread out the data are

Question 3

For a standard normal distribution, what is the mean & sd

Answer 3

mean = 0
SD = 1

Question 4

Z-score

Answer 4

reflects how many standard deviations above or below the mean a given value is

Question 5

Z-score equation

Answer 5

Z(𝑥)= (𝑥 − μ)/σ

Question 6

guideline that describes the percentage of data that falls within certain standard deviations from the mean for a normal distribution.

Answer 6

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

Question 7

Central Limit Theorem (CLT)

Answer 7

describes how the distribution of sample means becomes approximately normal (bell-shaped) as the sample size increases, regardless of the shape of the population distribution, provided the sample size is large enough.

Question 8

as sample size goes up what goes down? why?

Answer 8

the standard error.
because sample size (n) is the denominator of the equation for se

Question 9

as the standard deviation goes up what goes up? why?

Answer 9

the standard error.
SE is directly proportional to SD