A very strange university assigns zscores to students at the

A very strange university assigns z-scores to students at the end of each school term rather than the traditional 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 Translate each of the following z-scores to corresponding GPA scores: z = 2.0, z = -1.0, z = 0.5, z = -2.5 Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA? The top 16% of graduating students are awarded cum laude honors and the top 2.5% are awarded 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 GPAs at the university?

Solution

A)

As

x = u + z*sigma

Then, for z = 2.0:

x = 2.7 + 2.0*0.5 = 3.7 [answer]

For z = -1.0,

x = 2.7 + (-1.0)*0.5 = 2.2 [answer]

For z = -2.5,

x = 2.7 + (-2.5)*0.5 = 1.45 [answer]

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b)

For z = -1.6,

x = 2.7 + (-1.6)*0.5 = 1.9 [answer]

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c)

In z scores, using table/technology:

cum laude: z = 0.994457883
summa cum laude: z = 1.959963985 [ANSWERS]

In GPA\'s, as z = u + z*sigma,

cum laude: 3.197228942
summa cum laude: 3.679981992 [ANSWERS]

I assumed that the GPAs followed a normal distribution.