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```IM 3
Z-Score #3
Name ____________________
Comparing Test Scores. For the statistics test, the mean is 63 and the standard deviation is 7.0. For the biology test, the
mean is 23 and the standard deviation is 3.9. In #1-4, you are given the test scores of a student who took both tests.
a) Transform each test score to a z-score.
b) Determine on which test the student had a better score.
1. A student gets a 73 on the statistics test and a 26 on the biology test.
2. A student gets a 60 on the statistics test and a 20 on the biology test.
3. A student gets a 78 on the statistics test and a 29 on the biology test.
4. A student gets a 63 on the statistics test and a 23 on the biology test.
Find a z-score satisfying the following conditions.
5. 5% of the total area is to the left of z.
6. 1% of the total area is to the left of z.
7. 15% of the total area is to the right of z.
8. 25% of the total area is to the right of z
The Wechsler Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the
raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal
distribution:
9. What number represents the 65th percentile (what number separates the lower 65% of the
distribution)?
10. What number represents the 90th percentile?
11. What is the probability of getting a raw score between 28 and 38?
12. What is the probability of getting a raw score between 41 and 44?
Scores on the SAT form a normal distribution with   500 and   100 .
13. What is the minimum score necessary to be in the top 15% of the SAT distribution?
14. Find the range of values that defines the middle 80% of the distribution of SAT scores.
For a normal distribution, find the z-score that separates the distribution as follows:
15. Separate the highest 30% from the rest of the distribution.
16. Separate the lowest 40% from the rest of the distribution.
17. Separate the highest 75% from the rest of the distribution.
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