Download presentation

Presentation is loading. Please wait.

1
**Normal distribution and probability**

Introduction Normal Curve Mean Introducing Standard Deviation Standard Deviation and the Normal curve The Normal Distribution The Standard Normal Distribution Expected Value Inverse Normal Problems Probability Exam Questions Probability exam Answers Probability Theoretical Probability Equally Likely Outcomes Probability Trees Sampling without replacement Venn diagrams Experimental probability Long-Run relative frequency Simulation describe a simulation Simulation Question Simulation Exam Question L2 Normal Distribution & Probability M. Guttormson

2
**L2 Normal Distribution & Probability**

Introduction L2 Normal Distribution & Probability M. Guttormson

3
**L2 Normal Distribution & Probability**

Introduction L2 Normal Distribution & Probability M. Guttormson

4
**L2 Normal Distribution & Probability**

The Normal Curve Many sets of data collected in nature, industry, business and other situations fit what is called a normal distribution. This means: If the frequency of each piece of data were graphed, the curve would fit a symmetrical bell shape. Most measurements are near the middle The further away from the middle value (mean), the less frequent the occurrence. The general shape looks like this L2 Normal Distribution & Probability M. Guttormson

5
**L2 Normal Distribution & Probability**

The Normal Curve L2 Normal Distribution & Probability M. Guttormson

6
**L2 Normal Distribution & Probability**

Mean The mean is just the average of the numbers. It is easy to calculate: Just add up all the numbers, then divide by how many numbers there are. L2 Normal Distribution & Probability M. Guttormson

7
**Introducing Standard Deviation**

The Standard Deviation (σ) is a measure of how spread out numbers are. You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm. Let’s find out the Mean and the Standard Deviation. L2 Normal Distribution & Probability M. Guttormson

8
**Introducing Standard Deviation**

Answer: so the average height is 394 mm. Let's plot this on the chart: L2 Normal Distribution & Probability M. Guttormson

9
**Introducing Standard Deviation**

Calculate the Standard Deviation using your calculators. Now we can show which heights are within one Standard Deviation (147mm) of the Mean: So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small. Rottweillers are tall dogs. And Dachsunds are a bit short . L2 Normal Distribution & Probability M. Guttormson

10
**Standard Deviation and the Normal Curve**

One standard deviation away from the mean in either direction on the horizontal axis (the red area on the graph) accounts for somewhere around 68 percent of the people in this group. “Likely/probable” Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. “Very likely/very probable” Three standard deviations (the red, green and blue areas) account for about 99 percent of the people. “Almost certain” The total area under the curve adds to 1 (or 100%) L2 Normal Distribution & Probability M. Guttormson

11
**The Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

12
**The Normal Distribution**

95% 65km/h and 125km/h 16% 105km/h L2 Normal Distribution & Probability M. Guttormson

13
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

14
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

15
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

16
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

17
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

18
**The Standard Normal Distribution**

L2 Normal Distribution & Probability M. Guttormson

19
**The Standard Normal Distribution**

Notation For the same question, calculate the percentage of cars travelling more than 97km/h? What is the probability that X is greater than 97km/h It is the probability that Z is greater than 0.2 This is equal to 1 – probability that Z is greater than 0.2 This is equal to 1 – Which is 42.07% L2 Normal Distribution & Probability M. Guttormson

20
**L2 Normal Distribution & Probability**

Expected Value L2 Normal Distribution & Probability M. Guttormson

21
**Inverse Normal Problems**

L2 Normal Distribution & Probability M. Guttormson

22
**Inverse Normal Problems**

L2 Normal Distribution & Probability M. Guttormson

23
**Inverse Normal Problems**

L2 Normal Distribution & Probability M. Guttormson

24
**Equally Likely Outcomes**

Theta Exercise 22.01 L2 Normal Distribution & Probability M. Guttormson

25
**L2 Normal Distribution & Probability**

Probability Trees 0.4 0.6 Kauri Rimu 0.1 0.9 0.05 0.95 Returned Not Returned 0.04 0.36 0.03 0.57 L2 Normal Distribution & Probability M. Guttormson

26
**L2 Normal Distribution & Probability**

Probability Trees 0.4 0.6 Kauri Rimu 0.1 0.9 0.05 0.95 Returned Not Returned 0.04 0.36 0.03 0.57 L2 Normal Distribution & Probability M. Guttormson

27
**L2 Normal Distribution & Probability**

Probability Trees 0.4 0.6 Kauri Rimu 0.1 0.9 0.05 0.95 Returned Not Returned 0.04 0.36 0.03 0.57 L2 Normal Distribution & Probability M. Guttormson

28
**L2 Normal Distribution & Probability**

Probability Trees Action Where Key Word Multiply Sideways along branches “and” Add Vertically at ends of branches “or” L2 Normal Distribution & Probability M. Guttormson

29
**Sampling Without Replacement**

3/7 Blue Red 1/2 2/3 1/3 2/7 1/7 4/7 L2 Normal Distribution & Probability M. Guttormson

30
**L2 Normal Distribution & Probability**

Venn Diagrams Union (one or the other or both) Intersection (both only) L2 Normal Distribution & Probability M. Guttormson

31
**L2 Normal Distribution & Probability**

Venn Diagrams Complimentary Events P(A) is the probability inside the circle. P(A’) is the probability outside the circle. P(A) + P(A’)=1 Example: Probability that it rains tomorrow is 0.4. The probability that it does not rain tomorrow is 0.6 Mutually Exclusive Events Theta Chapter 22 Exercise 22.04 Intersecting Events L2 Normal Distribution & Probability M. Guttormson

32
**Long-run relative frequency**

L2 Normal Distribution & Probability M. Guttormson

33
**L2 Normal Distribution & Probability**

Simulation L2 Normal Distribution & Probability M. Guttormson

34
**How to describe a simulation**

Tool: Definition of the probability tool Statement of how the tool models the situation (Assign) “Generate random numbers using the random number key on a calculator and truncate. 12ran#+1=” “Designate numbers to colours of tee-shirts in the appropriate proportions. 1, 2 = blue 3, 4, 5 = red 6 = green 7, 8 = purple 9, 10 = yellow 11, 12 = black Trial: Definition of a trial Definition of a successful outcome of the trial “One trial would involve generating random numbers until there are seven outcomes representing each day of the week. Days need to be labelled Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday.” A successful trial would be if 3 or more of the same colour shirt appears in one trial (one week). L2 Normal Distribution & Probability M. Guttormson

35
**How to describe a simulation**

Results: Statement of how the results will be tabulated giving an example of a successful outcome and an unsuccessful outcome. Statement of how many trials should be carried out. “ A tick in the results column will indicate when 3 of the 7 random numbers generated represent the same colour tee-shirt. Repeat a minimum of 20 times.” Calculation: Statement of how the calculation needed for the conclusion will be done: Long run relative frequency = Number of successful results Number of trials Mean = Sum of trial results The probabilities will be calculated using: Number of successful results 20 L2 Normal Distribution & Probability M. Guttormson

36
**L2 Normal Distribution & Probability**

Simulation Question L2 Normal Distribution & Probability M. Guttormson

37
**Simulation Exam Question “T-shirts”**

L2 Normal Distribution & Probability M. Guttormson

38
**Simulation Exam Question “T-shirts”**

L2 Normal Distribution & Probability M. Guttormson

39
**Simulation Exam Question “Fair Cop”**

L2 Normal Distribution & Probability M. Guttormson

40
**Simulation Exam Question “Fair Cop”**

L2 Normal Distribution & Probability M. Guttormson

41
**Probability exam Questions**

QUESTION ONE Andrew collected a large sample of chest measurements from students of his year level. He found the chest measurements to be approximately normally distributed with a mean chest measurement of 86cm and a standard deviation of 3.5cm. (a) Calculate the probability that a randomly selected student from Andrew’s year level (i) would have a chest measurement between 86cm and 90cm (ii) would have a chest measurement less than 87.5cm (b) Andrew’s class has 34 students in it. How many of these students would you expect to have chest measurements of more than 89cm? L2 Normal Distribution & Probability M. Guttormson

42
**Probability exam Questions**

L2 Normal Distribution & Probability M. Guttormson

43
**Probability exam answers**

L2 Normal Distribution & Probability M. Guttormson

Similar presentations

OK

Cell Diameters and Normal Distribution. Frequency Distributions a frequency distribution is an arrangement of the values that one or more variables take.

Cell Diameters and Normal Distribution. Frequency Distributions a frequency distribution is an arrangement of the values that one or more variables take.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Pdf to ppt online converter online Download ppt on clauses in english grammar Ppt on summary writing techniques Ppt on land soil water natural vegetation and wildlife resources Ppt on magnetic effect of electric current Ppt on second law of thermodynamics for kids Ppt on total knee replacement Ppt on fair and lovely cream Mp ppt online form 2013 Ppt on earth and universe