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".

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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