A group of students (large group) took a test in mathematics and the final scores have a mean of 68 and a variance of 100. If the distribution of these scores is approximately normal, then what percent of the students: i. Scored higher than 75? ii. Should pass the test (scores ≥ 65)? iii. Should fail the test (scores < 65)?
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.
A group of students (large group) took a test in mathematics and the final scores have a
normal, then what percent of the students:
i. Scored higher than 75?
ii. Should pass the test (scores ≥ 65)?
iii. Should fail the test (scores < 65)?
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