If the grading policy is to give a grade of A to the top 5% of scores based on the Normal distribution with mean 72 and standard deviation 10, what is the cutoff for an A in terms of a standardized score? 64 93 54 76 71 100 62 53 80 72 Here are the z scores: Score z-value 64 -0.8 93 2.1 54 -1.8 76 0.4 71 -0.1 100 2.8 62 -1 53 -1.9 80 0.8 72 0
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.
If the grading policy is to give a grade of A to the top 5% of scores based on the
| 64 | 93 | 54 | 76 | 71 | 100 | 62 | 53 | 80 | 72 |
Here are the z scores:
| Score | z-value |
| 64 | -0.8 |
| 93 | 2.1 |
| 54 | -1.8 |
| 76 | 0.4 |
| 71 | -0.1 |
| 100 | 2.8 |
| 62 | -1 |
| 53 | -1.9 |
| 80 | 0.8 |
| 72 | 0 |
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