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Once again, my blog site is

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Presentation on theme: "Once again, my blog site is"— Presentation transcript:

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.

6

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.


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