Download presentation
Presentation is loading. Please wait.
1
Once again, my blog site is www.mathwithdillon.weebly.com
You should visit this site to get notes and assignments, check HW and WS, and check the calendar for assessment dates.
2
Come see me if you don’t understand a concept.
You should bring your worked homework problems so I can see what your mistake is. You have to attempt homework problems before I can help you. I don’t know how to help you unless I see some work from you.
3
Lesson #8: Normal Distribution
Accel Math III Unit #1: Data Analysis Lesson #8: Normal Distribution EQ: What are the characteristics of a normal distribution and how is probability calculated using this type of distribution?
4
Recall: Three Types of Distributions
Binomial Normal Geometric Normal Distributions --- created from continuous random variables
5
1. Symmetric, Bell-Shaped Curve and Uni-modal.
Characteristics of a Normal Distribution: 1. Symmetric, Bell-Shaped Curve and Uni-modal.
7
2. Mean, Median, Mode are equal and located at the middle of the distribution. Symmetric about the mean. Not skew.
8
3. The curve is continuous, no gaps or holes
3. The curve is continuous, no gaps or holes. The curve never touches or crosses the x-axis. The total area under the curve equals 1. Recall: Empirical Rule
9
Normal Distribution --- each has its own mean and standard deviation.
What are µ and σ in this normal distribution ?
10
Standard Normal Distribution --- mean is always 0 and standard deviation is always 1
STANDARDIZE
11
z-score --- the number of standard deviations above or below the mean
z = observed – mean or z = X - µ standard deviation σ Correlates to area under the curve. Area under the curve at that score z-score
12
Ex. In a study of bone brittleness, the ages of people at the onset of osteoporosis followed a normal distribution with a mean age of 71 and a standard deviation of 2.8 years. What z-score would an age of 65 represent in this study? | | | | | | | -2.14 | | | | | | | 65
13
Using Table A to Finding the Area under A Standard Normal Curve
14
Ex. Find the area under the curve to the left of z = -2.18.
| -2.18
15
Ex. Find the area under the curve to the left of z = 1.35.
| 1.35
16
Ex. Find the area under the curve to the right of z = 0.75.
We want the area to the RIGHT WHY?? | .75
17
Ex Find the area under the curve between z = -1.36 and z = 0.42.
P(-1.36 < z < 0.42) =_____ – =_____ 0.5759
18
Ex. Find the area under the curve between z = 1.60 and z = 3.3.
P(1.60 < z < 3.3) =_____ 0.0543 – =_____
19
In Class Practice Worksheet: Area Under the Standard Normal Curve
#1 - 11
20
What about finding a z-score when given area under the curve?
Ex. Determine the z-score that would give this area under the curve. -0.52
21
Ex. Determine the z-score that would give this area under the curve.
0.67
22
Ex. Determine the z-score that would give this area under the curve.
-1.13
23
In Class Practice Worksheet: Area Under the Standard Normal Curve
#12a – e only Practice Worksheet Calculating Area Using z-scores
24
Using the Graphing Calculator with Normal Distributions
Command and Arguments: When given a z-score, you are looking for area under the curve. normalcdf(low bound, high bound) normcdf(___, ____) P(z <-2.18) = _____ = 1.46%
25
normcdf(___, ____) -10 1.35 P(z < 1.35) = _____ 0.9115 = 91.15%
Ex. Find the area under the curve to the left of z = 1.35. normcdf(___, ____) P(z < 1.35) = _____ = 91.15% normcdf(___, ____) P(z > 0.75) = _____ = 22.66%
26
normcdf(___, ____) P(-1.36 < z < 0.42) = _____ 0.5758 = 57.58%
Ex Find the area under the curve between z = and z = 0.42. normcdf(___, ____) P(-1.36 < z < 0.42) = _____ = 57.58% normcdf(___, ____) P(1.60 < z < 3.3) = _____ = 5.43%
27
When given area, you’re looking for a z-score.
Use invnorm function under distributions. invnorm(% to the left)
28
1.64 0.95 0.67 0.25 0.75 Pay attention to what you write!
29
1.20 0.885 0.50 -1.15 1.15 0.125 0.375 0.375 0.125 or 0.875 Symmetric 0.50
30
***Remember invnorm and normcdf are calculator jargon
Do not write these functions on assessments as “work”. Must include probability statements.
31
Example Handout: Area Under the Standard Normal Curve #1 – 12
Assignment: Example Handout: Area Under the Standard Normal Curve #1 – 12 WS Calculating Area Using z-scores Go back and rework these using the calculator function.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.