At one university, the students are given z-scores at the...

At one university, the students are given z-scores at the end of each semester, which are based on mean of 2.7 and standard deviation of 0.5. a. Translate the following z-scores into GPAs: z = 1.0, z = -2.0, z = 0.75, z = 3.0 b. Students with z-scores below -1.8 are put on probation, what GPA corresponds to this probationary score. c. The president of the university wishes to graduate the top 15% of students with cum laude honours and the top 2.5% with summa cum laude honours. Where (approximately) should the limits be set in terms of z-scores? In terms of GPA? What assumption, if any, did you make about the distribution of GPAs? Hint: This is an approximate value, so the graphical representation of the Empirical rule would be quite helpful for this.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:05 In the question here, we are going to discuss about the g score formula.

00:09 So the z equal to the x minus the mean over the standard deviation.

00:14 Now in this question here we're given the mean equal to 2 .7, standard division equal to the 0 .5.

00:24 Now the first question a, as much you convert the g score into the gba score.

00:33 So the first one we have the z score equal to the 1 .0.

00:41 So i don't want to make sure here it will be the 1 .0 and therefore we have the 1 .0 it will equal to the x minus the beam will be the 2 .7 over the 0 .5.

00:54 From here we want to serve for the x then we get equal to the 1 point zero time with the 0 .5 and then plus the 2 .7 then we get equal to the 0 .5 equal to the 3 .2 and for the number 2 we have the z score equal to the minus 2 .0 and then from here we have the minus 2 .0 equal to the x we minus the 2 .7 over the 0 5.

01:27 From here the x it will equal to minus 2 .0 times with the 0 .5 plus 2 .7 and then we get equal to this will be the minus 1 and then equal to the 1 .7.

01:41 For the number 3 we have the z score equal to the 0 .75 and then we have the 0 .75 equal to the x minus the 2 .7 divide by the 0 .5 therefore the x it would equal to 0 .75 time with the 0 .5 plus 2 .7 and then we get equal to 25 plus 2 .7 equal to the 3 .075.

02:15 For the number 4 the zip score equal to the 3 .0.

02:20 Therefore we have the 3 .0 equal to the x minus 2 .7 over the 0.

02:27 5 and then we have x equal to the 3 .0 10m .5 plus 2 .7.

02:35 Don't get, plus 2 .7 equal to the 4 .2 and that will be the answer for the a...

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