1) Compute the z score corresponding to each of the following values of x
a. x=40, s=5, x with a bar=30
b. x=90, mean= 89, sigma=2
c. mean=50, sigma= 5, x =50
d. s=4, x=20, x with a bar =30
e. in parts a-d state whether the z score locates x within a sample or a population
f. in parts a-d state whether each value of x lies above or below the mean and by how many standard deviations
2) At one university the students are given z scores at the end of each semester rather than the traditional gpa's. the mean and standard deviation of all students cumulative gpa's on which the z-scores are based are 2.7 and .5 respectively
a. translate each of the following z scores to corresponding gpa: z=2.0, z=-1.0, z=.5, z=-2.5
b. student's with z scores below -1.6 are put on probation. what is the corresponding probationary GPa
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 should the limits be set in terms of z-scorses? In terms of gpa? What assumption did you make about the distribution of the gpa's?
Thanks for letting me work on your post. Here is my explanation:
1) z=(30-40)/5=-2. it means x is 2 standard deviations below the mean;
b) z=(90-89)/2=0.5. it means x is 0.5 standard deviation above the mean;
c) z=(50-50)/5=0. It means x is 0 standard deviation away from the mean (or same as the mean);
The solution compares z-scores in a population.