STA215H5 Study Guide - Fall 2018, Comprehensive Midterm Notes - Normal Distribution, Histogram, Unimodality
STA215H5
MIDTERM EXAM
STUDY GUIDE
Fall 2018
12.2.B&C Empirical rule<-> probabilities associated
•12.2.D&E z tables and pnormz and x →probabilities
•12.2.F&G z tables and pnormpercentiles →z and x
•12.2.H&I z tables and qnormprobabilities →z and x
•12.2.J histogram and qqplotto assess normality
•Maybe mention transformations
•Non-normal data that looks normal enough
Normal Distribution
•The most common distribution used in statistics
•Aka the Gaussian distribution
•Used in building confidence intervals
•Used in hypothesis testing
•It is the back bone of applied statistics!
By the end of this lesson you should be able to:
1.Locate probabilities on a z-table, given a z value.
2.Locatetheappropriatezvalue from a z-table, when
giventheprobability.
3.AppropriatelyplugintotheZ-score formula when given a word
problem.
4.Drawa picture of the curve (with the horizontal axis labelled) and
shade in the desired region when given a probability statement.
The Standard Normal Distribution
find more resources at oneclass.com
find more resources at oneclass.com
•Random variable, Z
•A bell curve
•Centre at z = 0
•Symmetry about z = 0
•Inflection points at z = ±1
•Area under curve =1
•Notation Z ~ N(0,1)
The curve is high in intervals around z = 0, so there is high probability
an observation of Z will be in an interval around 0.
•The curve is low in intervals around z = 3 and z = -3, so there is low
probability an observation of Z will be in an interval around 3 or -3.
Curve is a Histogram
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
12. 2. b&c empirical rule probabilities associated: 12. 2. d&e z tables and pnormz and x probabilities, 12. 2. f&g z tables and pnormpercentiles z and x, 12. 2. h&i z tables and qnormprobabilities z and x, 12. 2. j histogram and qqplotto assess normality, maybe mention transformations, non-normal data that looks normal enough. Normal distribution: the most common distribution used in statistics, aka the gaussian distribution, used in building confidence intervals, used in hypothesis testing, it is the back bone of applied statistics! By the end of this lesson you should be able to: 1. locate probabilities on a z-table, given a z value. 4. drawa picture of the curve (with the horizontal axis labelled) and shade in the desired region when given a probability statement. The standard normal distribution: random variable, z, a bell curve, centre at z = 0, symmetry about z = 0, inflection points at z = 1, area under curve =1, notation z ~ n(0,1)
