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8.7 Applications of the Normal Distribution
Bell-curve reasoning turned on real data such as test scores, heights, and manufacturing tolerances, each answered by standardizing first.
Contemporary Mathematics, 8.7 Applications of the Normal Distribution
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2 exercises
8.7 Exercise 1
According to the Digest of Education Statistics, composite scores on the SAT have mean 1060 and standard deviation 195, while composite scores on the ACT have mean 21 and standard deviation 5.
- At what percentile would an SAT score of 990 fall?
- What is the z-score of an ACT score of 27?
- Which is better: a score of 1450 on the SAT or 29 on the ACT?
2.5
8.7 Exercise 3
Let’s say we flip a coin 64 times and count the number of heads.
- What would be the mean of the corresponding distribution?
- What would be the standard deviation of the corresponding distribution?
- Suppose we got 25 heads, which seems a little low. At what percentile would 25 heads fall?
2.5
Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.