Download Chapter 5 Normal Probability Distributions

Chapter 5
Normal Probability Distributions
Chapter 5
Normal Probability Distributions
Section 5-3 – Normal Distributions: Finding Values
A. We have learned how to calculate the probability given an x-value or
a z-score.
In this lesson, we will explore how to find an x-value or z-score when
given the probability (cumulative area under the curve).
1. The cumulative area under the curve is a direct variation of the zscore; as the z-score goes up, so does the cumulative area.
a. Because this is a one to one function, it also has an inverse
function.
1) Lucky for us, the calculator has an operation to find the
inverse of the cumulative area.
a) 2nd VARS invNorm(probability) = z-score.
b) 2nd VARS invNorm(probability, mean, standard deviation)
= x-value
Chapter 5
Normal Probability Distributions
Section 5-3 – Normal Distributions: Finding Values
2. Once you have the z-score, you can also find the matching xvalue.
a. If we take the formula for finding the z-score and solve it for x,
we get that x = μ + zσ.
1) In other words, x is equal to the mean plus the z-score
times the standard deviation.
B. The key here is going to be using the correct area under the curve to
find the z or x value that we are looking for.
1. Practice will make this a LOT easier.
a. As a general rule, if we want the area below a given
percentile, we use the given percentile.
b. If we want the area above a given percentile, we subtract the
given percentile from 1 and use the answer.
(Complement Rule)
Chapter 5
Normal Probability Distributions
Section 5-3 – Examples
Page 266, #1-3 and 13, 14, and 16
Find the z-score that corresponds to the given cumulative area or
percentile.
1) 0.7580
InvNorm(.7580,0,1) = .700
2) 0.2090
InvNorm(.2090,0,1) = -.810
3) 0.6331
InvNorm(.6331,0,1) = .340
13) P1
InvNorm(.01,0,1) = -2.326
14) P15
InvNorm(.15,0,1) = -1.036
16) P55
InvNorm(.55,0,1) = 1.126
Your Assignments are:
Classwork:
Pages 266-267 #25-38 All
Homework:
Pages 267-268 #39-46 All