# Unit_5_lesson_5_redone

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### Unit 5: Distributional ShapeLesson 5:Probability and the Normal Curve :

Unit 5: Distributional ShapeLesson 5:Probability and the Normal Curve EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

### Normal curve = Exact percentages of area under the curve :

Normal curve = Exact percentages of area under the curve Exact percentages = Exact probabilities Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Randomly draw one score :

Randomly draw one score Prob. of Z <=0 .50 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### In a normal curve, we can use the Z score to identify the probability of obtaining a score < or > the score in question. :

In a normal curve, we can use the Z score to identify the probability of obtaining a score < or > the score in question. Area under the curve represents probability of observations. Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### IQ Test: Your Z = 1.00 :

IQ Test: Your Z = 1.00 .50 + .34 ~ ~ .84 1.00 - .84 ~ ~ .16 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### But what if the Z score isn’t a nice round #? :

But what if the Z score isn’t a nice round #? * For any point in the distribution there is a probability above and below the Z score. * We can use a table to calculate the probabilities. Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### GRE verbal = 550 :

GRE verbal = 550 Probability of scoring better than 550? Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Use an Area under Standard Normal Curve Table for Values of Z – Table C.1: Hinkle, Wiersma, & Jurs (1998) :

Use an Area under Standard Normal Curve Table for Values of Z – Table C.1: Hinkle, Wiersma, & Jurs (1998) *Table gives:1) Area between (Z=0) and Z.2) Area beyond Z (into the tail). Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Probability of scoring better than Z = .50? :

Probability of scoring better than Z = .50? Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Slide 10:

Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Probability of scoring better than Z = -1.38? :

Probability of scoring better than Z = -1.38? .9162 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Tabled Z values can be positive or negative. :

Tabled Z values can be positive or negative. Can calculate exact probabilities given a Z score. Assumes a normal distribution for your scores. Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Slide 13:

Dr. Robin K. Henson © 2002 University of North Texas Go to next slide for answer. Q: You have just received your midterm exam back and earned a Z score of -.23. Assuming the students’ scores were normally distributed, you did better than what proportion of other students? a. .409 b. .091 c. .591 d. .909 e. None of the above. Click mouse to continue

Answer a. Yes, the area beyond a Z = .23 to the tail is .409 per the Standard Normal Curve table. Note that you have to consider the absolute value of the tabled areas because the tabled areas apply to both sides of the normal distribution of Z scores (i.e., the distribution is perfectly symmetrical). b. No, this is the area between Z and the mean for Z = .23. We care about the area in the tail to find out the proportion you did better than. c. No, this is the proportion higher than Z = .23, and is irrelevant here. d. No, this is irrelevant. e. No, (a) is correct. Click mouse to go to next slide.

### Slide 15:

Dr. Robin K. Henson © 2002 University of North Texas Go to next slide for answer. Q: Because she likes to show off her immense knowledge of statistics, your obnoxious classmate tells you that you did better than 79.1% of the other students’ scores (which happen to be normally distributed) on your midterm exam. If your obnoxious classmate is right, this means your Z score must have been: a. .791 b. .810 c. .209 d. .190 e. None of the above. Click mouse to continue 