Explanation Given information: Chemistry is taught at five high schools in the Santa Rosa Unified School District. The district has received a grant of 100 microscopes, which are to be apportioned to the five high schools, based on each school’s chemistry population. Use the following data. School # Students # Chemistry Students Elsie Allen 1 , 524 90 Maria Carrillo 1 , 687 215 Montgomery 1 , 755 268 Piner 1 , 519 133 Santa Rosa 1 , 797 84 TOTAL 8 , 282 790 Total number of microscopes is 100 . Total number of chemistry students is 790. Total number of high schools is 5 . Formula used: STANDARD DIVISOR = TOTAL POPULATION NUMBER OF SHARES STANDARD QUOTA = TOTAL POPULATION STANDARD DIVISOR Calculation: Total number of microscopes is 100 . Total number of high schools is 5 . Total number of chemistry students is 790 . Given below are four types of apportioned paradoxes: 1. Alabama Paradox 2. Population paradox 3. New state paradox 4. Quota rule Alabama paradox occurs if there is a reapportionment in which an increase in the total number of microscopes results in a loss in the microscopes for some school. Given number of microscopes is 100 . There is no increase in microscopes; therefore, Alabama paradox does not occur. Population paradox occurs if one high school loses microscopes to another school even though its percent increase in the chemistry students is larger. Given number of chemistry students is 790 . There is no increase in the number of chemistry students in any of the high schools; therefore, population paradox does not occur. New state paradox occurs if the addition of a new high school changes the apportionment of another high school. Given number of high schools is 5 . There is no increase in total high schools; therefore, new state paradox does not occur. As per quota rule, apportionment must be either the lower or upper quota. Total number of chemistry students is 790 . Total number of microscopes is 100 . Therefore, standard divisor is d = 790 100 = 7.9 . Divide the population of chemistry students of each school by standard divisor ( d ) to find the standard quota ( q ) . Round the standard quota down to get the lower quota, and round the standard quota up to get the upper quota. School # Chemistry Students Standard quota ( q ) Lower quota Upper quota Elsie Allen 90 90 7

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 17.CR, Problem 19CR

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If any apportionment paradoxes occur, when the district received a grant of 100 microscopes which are to be distributed to the five high schools based on the number of chemistry students.

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Nature of Mathematics (MindTap Course List)

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If any apportionment paradoxes occur, when the district received a grant of 100 microscopes which are to be distributed to the five high schools based on the number of chemistry students.

Solution Summary: The author explains that the Santa Rosa Unified School District has received a grant of 100 microscopes, which are to be distributed to the five high schools based on the number of chemistry students.

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If any apportionment paradoxes occur, when the district received a grant of 100 microscopes which are to be distributed to the five high schools based on the number of chemistry students.

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