A teacher informs his advanced music theory class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 42 and a standard deviation of 7.9. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 42.5, but not a 41.83.) The grades are curved according to the following scheme. Find the numerical limits for each letter grade. Letter Scheme Interval A Top 15% B Scores above the bottom 74% and below the top 15% C Scores above the bottom 26% and below the top 26% D Scores above the bottom 15% and below the top 74% F Bottom 15%
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The grades are curved according to the following scheme. Find the numerical limits for each letter grade.
| Letter | Scheme | Interval |
|---|---|---|
| A | Top 15% | |
| B | Scores above the bottom 74% and below the top 15% |
|
| C | Scores above the bottom 26% and below the top 26% |
|
| D | Scores above the bottom 15% and below the top 74% |
|
| F | Bottom 15% |
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