1. The Normal Distribution
Chapter 2
Part 2

2. Iliana’s Grade
After 5 weeks of class Iliana must transfer from a stat class at Moore HS to this class. Last week was the chapter 1 test in both classes. Iliana scored a 61 out of 70 (87%). Let’s say our test was out of 100 points. What score should she be given?

3. Iliana’s claim
Iliana claims that her test at MHS was harder than our test.
Does your previous method of assigning a grade take in consideration difficulty?
If we have all of the data, what important facts can we utilize to improve our assignment of Iliana’s grade?

4. Important Facts
Maximum possible on our test was 100 pts while Moore’s test was 70 pts.
Mean score on Moore’s test was 50.5 pts while our test was 77.2 pts.
Standard deviation on Moore’s test was pts while ours was 8.1 pts.
Test scores from both high schools tend to be normally distributed.
How will we fairly assign Iliana’s score?

5. Moore’s distribution
Iliana
50.5

6. Moore’s and Westmoore’s distributions
Iliana’s score
– class average
standard deviation
50.5
Iliana
– 50.5 61
5.3
1.98
77.2
Iliana
How can we find Iliana’s relative position?

7. Formula
What is the formula to find the relative position for any distribution?
Iliana’s score
– class average
standard deviation
z–score=

8. Formula
A z-score is how many standard deviations the point is from the mean
z–score=

9. First quiz: Second quiz:
1. Suppose as student has taken two quizzes in a statistics course. On the first quiz the mean score was 32, the standard deviation was 8, and the student received a 44. The student obtained a 28 on the second quiz, for which the mean was 23 and the standard deviation was 3. If test scores are approximately normal, on which quiz did the student perform better relative to the rest of the class?
First quiz:
Second quiz:

10. 3. A married couple is employed by the same company
3. A married couple is employed by the same company. The husband works in a department for which the mean hourly rate is $12.80 and the standard deviation is $ His wife is employed in a department where the mean rate is $13.50 and the standard deviation is $1.80.
Relative to their departments, which is better paid if the husband earns $14.60 and the wife earns $15.75?
Husband:
Wife:

11. What percentile is the husband located in his department?

12. What percent of employees in the wife’s department earn better than her?

13. What would the wife need to earn to match her husband’s relative position?
The wife would need to earn $16.20 to match the husband’s relative position.

14. If the husband wanted to earn in the 95th percentile, how much should he earn per hour?
Need a z-score of 1.65!

15. The husband will need to earn at least $14
The husband will need to earn at least $14.78 to be in the 95th percentile.

16. #6
– 2 2

17. 5.5% 94.5% 89% 44.5% z-score = –1.60 z-score = 1.60
The middle 89% of the data ranges from to ppb.