4 & 5. Statistics, Quality Assurance and Calibration Methods
The Gaussian Distribution
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From EXAMPLE 1, determine the percentage of final grades that would lie between 88 to 92.
A
5.36 %
B
5.33 %
C
5.39 %
D
5.49 %
Verified step by step guidance1
Identify the distribution type of the final grades. If it's a normal distribution, you can use the properties of the normal distribution to find the percentage of grades between two values.
Determine the mean (μ) and standard deviation (σ) of the distribution from EXAMPLE 1. These values are crucial for calculating probabilities in a normal distribution.
Convert the raw scores (88 and 92) to z-scores using the formula: z = (X - μ) / σ, where X is the score you are converting.
Use the standard normal distribution table (z-table) to find the probability corresponding to each z-score. This will give you the cumulative probability for each score.
Subtract the cumulative probability of the lower z-score (for 88) from the cumulative probability of the higher z-score (for 92) to find the percentage of grades that lie between 88 and 92.
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