A university wants to divide its students into three groups of "weak", "moderate", and "strong" based on their placement test grades so that those students whose grades are less than X are considered as "weak", between X and Y are considered as "moderate", and those who get a mark greater than Y are considered as "strong". The placement test results show an average of 79 with a standard deviation of 5. Find X and Y so that around 33% of the students are categorized as "weak" and 22% of students are categorized as "strong".
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 university wants to divide its students into three groups of "weak", "moderate", and "strong" based on their placement test grades so that those students whose grades are less than X are considered as "weak", between X and Y are considered as "moderate", and those who get a mark greater than Y are considered as "strong". The placement test results show an average of 79 with a standard deviation of 5. Find X and Y so that around 33% of the students are categorized as "weak" and 22% of students are categorized as "strong".
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