normal distributions vocab

normal dist, standard normal dist, and t-dist

distribution

a listing of all the possible values that a characteristic can take + the number/% of times tat each value occurs

how to describe a distribution

1. shape
2. center
3. spread
4. unusual features

normal distribution

1. shape: symmetric bell-shaped curve
2. center: defined by µ
3. spread: defined by σ
4. unusual features: none

notation for normal distributions

X \~ N (µ, σ)

* read as X is distributed normal with mean µ and stdvt σ

area %s under a normal distribution curve

* within +/- 1 σ: 68%
* within +/- 2σ: 95%
* within +/- 3σ: 99.7%

what is a standard normal distribution

special type of normal distribution that has a µ=0 and σ=1; denoted by Z

when is a t-distribution used

when the population stdvt isn’t known

features of t-distributions

1. shape: symmetric bell shaped curve
2. µ=0
3. spread: stdvt greater than or equal to 1
4. unusual features: none

calc: to find probability of a normal distribution

2: normalcdf(lower, upper, mean, stdvt)

calc: to find a value of a normal distribution

3: invnorm(area, mean, stdvt)

calc: to find probability of a t-distribution

6: tcdf(lower, upper, df)

calc: to find a value of a t-distribution

4:invt(area, mean, stdvt)

types of probability problems + parts

* greater than: lower value, 1E99, mean, stdvt
* between: lower value, upper value, mean, stdvt
* less than: -1E99, upper value, mean, stdvt

types of value problems + parts

* greater than: area (1 - probability), mean, stdvt
* between: area (probability + 1-probability), mean (x2), stdvt (x2)
* less than: area (probability), mean, stdvt