Question

In: Statistics and Probability

INDIAN STUDENTS DATA FILE (MINITAB) Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3...

INDIAN STUDENTS DATA FILE (MINITAB)

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
GRE Score 500 0 316.47 0.505 11.3 290 308 317 325 340
TOEFL Score 500 0 107.19 0.272 6.08 92 103 107 112 120
CGPA 500 0 8.5764 0.027 0.6048 6.8 8.1225 8.56 9.04 9.92
  1. What is the probability of students between CGPA 8 and 9?
  2. What is the probability of students above GRE 325 score?
  3. What is the GRE score middle 50% students?
  4. What is the TOEFL score of top 10% students?
  5. What is the CGPA of top 10% students?

Solutions

Expert Solution

a) probability of students between CGPA 8 and 9 = 68%

( because the mean is 8.5764 with ths standard deviation 0.6048. And according to empirical rule 68% of the data lie between 0ne standard deviation of the mean )

b)probability of students above GRE 325 score = 25%

( Because the third quartile is 325 that means that 75% of the data is below 325 and 25% is above 325)

c)GRE score middle 50% students = Median = 317

d)TOEFL score of top 10% students

Mean =107.19

Standard deviation, = 6.08

For top 10% we need to find the 90th percentile

P( Z < z ) = 0.9

P( Z < 1.282) = 0.9

z = 1.282

= 1.282

= 1.282

X = 107.18 + 6.08 * 1.282

X= 114.97

Hence , TOEFL score of top 10% students is 114.97

e)

CGPA of top 10% students

Mean =8.5764

Standard deviation, = 0.6048

For top 10% we need to find the 90th percentile

P( Z < z ) = 0.9

P( Z < 1.282) = 0.9

z = 1.282

= 1.282

= 1.282

X = 8.5764 + 0.6048 * 1.282

X= 9.35

Hence CGPA of top 10% students is 9.35

orchestra answered 2 years ago
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