At one university, the students are given z-scores at the end of each semester, rather than the traditional GPAS. The mean and standard deviation of all students' cumulative GPAS, on which the z-scores are based, are 2.6 and 0.4, respectively. Complete parts a through c. a. Translate each of the following z-scores to corresponding GPA scores: z= 2.0, z= - 1.0, z= 0.5, z= - 2.5. Translate z = 2.0 to the corresponding GPA score. GPA = (Type an integer or a decimal.) Translate z = - 1.0 to the corresponding GPA score. GPA = (Type an integer or a decimal.) %3D Translate z = 0.5 to the corresponding GPA score. GPA = (Type an integer or a decimal.) Translate z= - 2.5 to the corresponding GPA score. GPA = (Type an integer or a decimal.) b. Students with z-scores below - 1.6 are put on probation. What is the corresponding probationary GPA? GPA = (Round to the nearest tenth as needed.) c. The president of the university wishes to graduate the top 16% of the students with cum laude honors and the top 2.5% with summa cum laude honors. Where (approximately) should the limits be set in terms of z-scores? In terms of GPAS? What assumption, if any, did you make about the distribution of the GPAS at the university? O A. z> - 1.0 and - 2.0; GPA > 2.2 and 1.8; mound-shaped, symmetric B. z> 1.0 and 2.0; GPA > 3.0 and 1.8; mound-shaped, asymmetric C. z>1.0 and 2.0; GPA> 3.0 and 3.4; mound-shaped, symmetric D. z= 1.0 and 2.0; GPA > 3.4 and 3.0; the shape of distribution not important

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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At one university, the students are given z-scores at the end of each semester, rather than the traditional GPAS. The mean and standard deviation of all students' cumulative GPAS, on which the z-scores are based, are 2.6 and 0.4, respectively.
Complete parts a through c.
a. Translate each of the following z-scores to corresponding GPA scores: z= 2.0, z= - 1.0, z= 0.5, z= - 2.5.
Translate z = 2.0 to the corresponding GPA score.
GPA =
(Type an integer or a decimal.)
Translate z = - 1.0 to the corresponding GPA score.
GPA = (Type an integer or a decimal.)
%3D
Translate z = 0.5 to the corresponding GPA score.
GPA =
(Type an integer or a decimal.)
Translate z= - 2.5 to the corresponding GPA score.
GPA =
(Type an integer or a decimal.)
b. Students with z-scores below - 1.6 are put on probation. What is the corresponding probationary GPA?
GPA = (Round to the nearest tenth as needed.)
c. The president of the university wishes to graduate the top 16% of the students with cum laude honors and the top 2.5% with summa cum laude honors. Where (approximately) should the limits be set in terms of z-scores? In terms of GPAS?
What assumption, if any, did you make about the distribution of the GPAS at the university?
O A. z> - 1.0 and - 2.0; GPA > 2.2 and 1.8; mound-shaped, symmetric
B. z> 1.0 and 2.0; GPA > 3.0 and 1.8; mound-shaped, asymmetric
C. z>1.0 and 2.0; GPA> 3.0 and 3.4; mound-shaped, symmetric
D. z= 1.0 and 2.0; GPA > 3.4 and 3.0; the shape of distribution not important

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