3) (20 points) Graduate admissions at a particular university require applicants
ID: 3024308 • Letter: 3
Question
3) (20 points) Graduate admissions at a particular university require applicants to take the GRE. Hong, June and Eduardo are three applicants to the same graduate program. Scores are valid for several years, in 2011 the GRE changed the scale of scores from 200-800 to 130-170. Each applicant took the exam during a different year. Hong took the exam prior to the new scoring system, whereas June and Eduardo took the exam after the 2011 switch.
The table below summarizes each of their scores:
Applicant
Applicants Score
Year
Average
Standard Deviation
Hong
460
2010
480
90
June
165
2011
154
8
Eduardo
163
2013
148
7
The distribution of GRE scores for each year is assumed to be normally distributed with the associated mean and standard deviation.
a. (5 points) Why does it not make sense to compare the scores of the applicants in their given form?
b. (6 points) Calculate a z score for each participant. Which of the students is the best applicant based solely on their GRE score?
:
Applicant
Z score
Hong
June
Eduardo
c. (6 points) For first consideration to the graduate school, a student’s score must be at or above the 90th percentile. Which, if any, of the students made this cutoff? Calculate the percentile of each.
Applicant
Percentile
Hong
June
Eduardo
d. (3 points) Suppose in 2012 the middle 95% of GRE scores were from 135 to 165, assuming the distribution of scores is normal what is the mean and standard deviation? Hint: Draw the distribution and use the 68-95-99.7 Rule.
Applicant
Applicants Score
Year
Average
Standard Deviation
Hong
460
2010
480
90
June
165
2011
154
8
Eduardo
163
2013
148
7
Explanation / Answer
A)
Because they took the eams under different scoring systems.
***************
b)
As z = (x-u)/sigma, then:
Hong: z = (460-480)/90 = -0.222222222 [ANSWER]
June: z = (165-154)/8 = 1.375 [ANSWER]
Eduardo: z = (163-148)/7 = 2.142857143 [ANSWER]
Hence, EDUARDO IS THE BEST APPLICANT.
*****************
c)
Using a z distribution table/technology,
Hong: 41.21th percentile
June: 91.54th percentile
Eduardo: 98.39th percentile
Hence, JUNE AND EDUARDO MADE IT TO THE 90TH PERCENTILE ABOVE.
*****************
D)
The middle 95% are 2 standard deviations above and below the mean.
The mean is midway 135 and 165,
Mean = (135 + 165)/2 = 150 [ANSWER]
As 165 is 2 standard deviations above the mean, then
standard deviation = (165-150)/2 = 7.5 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.