Every year, a major university assigns Class A to ~16 per cent of its mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure to the remaining 16 per cent. The figures are repeated regardless of the variation in the actual performance in a given year. A graduating student tries to make sense of such a practice. She assumes that the individual candidate's scores X,....x, are independent variables that differ only in mean values EX,, so that 'centred' scores X, - EX, have the same distribution. Next. she considers the average sample total score distribution as approximately N(u. o²). Her guess is that the above practice is related to a standard partition of students' total score values into four categories. Class A is awarded when the score exceeds a certain limit, say a, Class B when it is between b and a, Class C when between c and b and Class D or failure when it is lower that c. Obviously, the thresholds c, b and a may depend on u and o. After a while (and using tables), she convinces herself that it is indeed the case and manages to find simple formulas giving reasonable approximations for a, b and c. Can you reproduce her answer?
Every year, a major university assigns Class A to ~16 per cent of its mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure to the remaining 16 per cent. The figures are repeated regardless of the variation in the actual performance in a given year. A graduating student tries to make sense of such a practice. She assumes that the individual candidate's scores X,....x, are independent variables that differ only in mean values EX,, so that 'centred' scores X, - EX, have the same distribution. Next. she considers the average sample total score distribution as approximately N(u. o²). Her guess is that the above practice is related to a standard partition of students' total score values into four categories. Class A is awarded when the score exceeds a certain limit, say a, Class B when it is between b and a, Class C when between c and b and Class D or failure when it is lower that c. Obviously, the thresholds c, b and a may depend on u and o. After a while (and using tables), she convinces herself that it is indeed the case and manages to find simple formulas giving reasonable approximations for a, b and c. Can you reproduce her answer?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Every year, a major university assigns Class A to ~16 per cent of its
mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure
to the remaining 16 per cent. The figures are repeated regardless of the variation in the
actual performance in a given year.
A graduating student tries to make sense of such a practice. She assumes that the
individual candidate's scores X,....x, are independent variables that differ only in
mean values Ex,. so that 'centred' scores X, - EX, have the same distribution. Next.
she considers the average sample total score distribution as approximately N(u. o). Her
guess is that the above practice is related to a standard partition of students' total score
values into four categories. Class A is awarded when the score exceeds a certain limit,
say a, Class B when it is between b and a, Class C when between c and b and Class D
or failure when it is lower that c. Obviously, the thresholds c, b and a may depend on u
and or.
After a while (and using tables), she convinces herself that it is indeed the case and
manages to find simple formulas giving reasonable approximations for a, b and c. Can
you reproduce her answer?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4524551d-924d-4411-b51e-e6589e3b3cbe%2F528ae2a9-6fad-4967-a896-24b0517ef17a%2Fi3vfqmy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Every year, a major university assigns Class A to ~16 per cent of its
mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure
to the remaining 16 per cent. The figures are repeated regardless of the variation in the
actual performance in a given year.
A graduating student tries to make sense of such a practice. She assumes that the
individual candidate's scores X,....x, are independent variables that differ only in
mean values Ex,. so that 'centred' scores X, - EX, have the same distribution. Next.
she considers the average sample total score distribution as approximately N(u. o). Her
guess is that the above practice is related to a standard partition of students' total score
values into four categories. Class A is awarded when the score exceeds a certain limit,
say a, Class B when it is between b and a, Class C when between c and b and Class D
or failure when it is lower that c. Obviously, the thresholds c, b and a may depend on u
and or.
After a while (and using tables), she convinces herself that it is indeed the case and
manages to find simple formulas giving reasonable approximations for a, b and c. Can
you reproduce her answer?
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