PE1-SS21: Using Z-scores For Grades 3: At one university, the students are given z-scores at the end of each semester rather than the traditional Great Point Average, (GPAS). The mean and standard deviation of all students' cumulative GPAS, on which the z-scores are based, are 2.7 and 0.5, respectively. 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 lower limits be set in terms of z-scores for each of the honors? HINT: Assume empirical rule applies. Oz-3.2 for cum laude and z = 3.7 for summa cum laude Oz= 1.0 for cum laude and z = 2.0 for summa cum laude Oz-2.5 for cum laude and z - 2.95 for summa cum laude Oz-2.0 for cum laude and z 3.0 for summa c cum laude z= 2.2 for cum laude and z- 2.95 for summa cum laude

PE1-SS21: Using Z-scores For Grades 3: At one university, the students are given z-scores at the end of each semester rather than the traditional Great Point Average, (GPAS). The mean and standard deviation of all students' cumulative GPAS, on which the z-scores are based, are 2.7 and 0.5, respectively. 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 lower limits be set in terms of z-scores for each of the honors? HINT: Assume empirical rule applies. Oz-3.2 for cum laude and z = 3.7 for summa cum laude Oz= 1.0 for cum laude and z = 2.0 for summa cum laude Oz-2.5 for cum laude and z - 2.95 for summa cum laude Oz-2.0 for cum laude and z 3.0 for summa c cum laude z= 2.2 for cum laude and z- 2.95 for summa cum laude

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Concept explainers

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.

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Question

PE1-SS21: Using Z-scores For Grades 3: At one university, the students are given z-scores at the end of each semester rather than the
traditional Great Point Average, (GPAS). The mean and standard deviation of all students' cumulative GPAS, on which the z-scores are
based, are 2.7 and 0.5, respectively.
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 lower limits be set in terms of z-scores for each of the honors? HINT: Assume empirical
rule applies.
Oz- 3.2 for cum laude and z- 3.7 for summa cum laude
Oz= 1.0 for cum laude and z= 2.0 for summa cum laude
Oz- 2.5 for cum laude and z - 2.95 for summa cum laude
Oz- 2.0 for cum laude and z- 3.0 for summa cum laude
Oz- 2.2 for cum laude and z - 2.95 for summa cum laude

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