Normal Curve (using the Z/Normal Chart)

Please make a separate sketch for each question!!. Put all of the information and answers on your pictures (percents inside the curve, z-scores under the curve, mean and raw scores under the curve...).

A. (determining exact percentages, not approximations, from z scores using the Z/Normal Chart) An education researcher has been studying test anxiety using a particular measure, which she administers to students prior to midterm exams. On the measure, she has found that the distribution of scores follows a 'normal' curve pattern. Using a Normal/Z chart, determine what percentage of students have scores:

1) below z = 1.5

2) below z = -1.5

3) above z = 2.1

4) above z = -.45

5) between z = -1.68 and z = -2.78

_93.32%_ _6.68%__ _1.79%__ _67.36%_

_4.38%__

B. (determining exact z scores from percentages, using the Z/Normal Chart)

Assuming a normally distributed set of scores for a Spanish test, what z score corresponds to (is the cutoff for) the following parts of the distribution:

6) top 15%

7) bottom 30%

8) top 5%

9) 90th percentile __+1.28__

10) the middle 60% (two answers) __-.84___ and _+.84__

C. (going from percentage to z-score to raw score)

Consider a medical test for which M = 200 and SD = 40. If the results are normally distributed, what (raw) score would a patient need to have, to be in the:

_+1.04_ _-.52__

_+1.65_

11) bottom 40% __190_

12) 80th percentile __233.6_

13) top 1% __293.2_

14) 33rd percentile __182.4__

15) extreme 5% (two answers: cutoff for top 2.5% and bottom 2.5%)

_121.6_ and _278.4_

D. (going from raw score to z-score to percentage)

Assuming that you had a test for which the results fit a normal curve, the mean is 70 and thestandard deviation is 8, what percent of students have scores:

16) below a 74? 69.15%

17) below a 60? 10.56%

18) above an 82? 6.68%

19) between 74 and 82? _24.17%_

20) between 66 and 74? _38.30%_