# Statistics

At one university, the students are given z-scores at the end of each semester instead of traditional GPA's. The mean and standard deviation of all the student' culmulative GPA's, on which the z-scores are based, are 2.7 and .5 respectively.

i understand how to translate the pas given the z-scores; however, i don't understand this question:

the president of the university wishes to graduate the top 16% of students with laude honors and the top 2.5% with summa laude honors. where should the limits be set in terms of z-scores [approx]? in terms of GPAs? what assumption if any did you make about the distribution of the GPAs at the university?

am i supposed to assume that there's a normal distribution? i don't understand how to get the answers to this question.
thank you.

1. 👍 0
2. 👎 0
3. 👁 733
1. oh wait...should use the 97.5 percentile to get the answer to the 2.5% top students?? because they wouldn't have negative z-scores, right?

1. 👍 0
2. 👎 0
2. Yes, assume a normal distribution.
100 - 2.5 = 97.5%
so any F(z) > .975 gets Summa
My table of z versus F(z) is pretty crude.
for example it has entries
z = 1.9 when F(z) = .971
z = 2.0 when F(z) = .977
We know that somewhere between z = 1.9 and z = 2.0, F (z) = .975
Say maybe any z over 1.95 gets summa.
Now do the same thing for F(z) = 1-.16 = .84
find z for f(z) = .84 (z around 1.0)
any z between there and 1.95 gets laude

1. 👍 0
2. 👎 0
3. Yes

1. 👍 0
2. 👎 0

## Similar Questions

1. ### statistics

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students

2. ### English

Which sentence is preferable? A. A student must see their advisor before registering for the following semester. B. A student must see his advisor before registering for the following semester. C. Students must see their advisor

3. ### Economics

Suppose a university decides to alter its tuition schedule by separating its students based on how many years of college they have completed. Most university programs require four years to complete. First-year students would get a

4. ### Statistics

Among first year students at a certain university, scores on the Verbal SAT follow the normal curve; the average is around 550 and the SD is about 100. a) what percentage of these students have scores in the range 400 to 700? b)

1. ### Information Technology

Develop an algorithm, flow chart and pseudocode that accept as input three unit test scores and a project score for seven students. The algorithm, flow chart and pseudocode should accept seven examination scores. The students's

2. ### statistics

The bottom 30% students failed an end of semester exam. The mean for the the test was 120 and the standard deviation was 17. What was the passing score?

3. ### Psychology, statistics

On a measure of artistic ability, the mean for college students in New Zealand is 150 and the standard deviation is 25. Give the z scores for new Zealand college students who score (a) 100, (b) 120 and (c) 140. Give a raw scores

4. ### Computer science

need help how do this program. Use the top-down modular approach and pseudocode to design a suitable program to solve it. Alberta Einstein teaches a business class at Podunk University. To evaluate the students in this class, she

1. ### statistics

4. The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the examination, what is the lowest score, to the nearest whole number,

2. ### statistics

Ten members of a fraternity take a statistics course. Here are their scores on the first exam in the course. 61,74,47,60,62,63,65,79,55,85. In all 135 students took the exam. The third quartile for all 135 scores was 69. How many

3. ### MATH URGENT!!!!

An investigator was interested in studying the effect of taking a course in child development on attitudes toward childrearing. At the end of the semester, the researcher distributed a questionnaire to students who had taken the

4. ### econ

Consider the following costs that a student incurs by attending a public university for one semester: \$3,000 for tuition, \$1,000 for room and board, \$500 for books and \$3,000 in after-tax wages lost that the student could have