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

What is the probability of students between CGPA 8 and 9?
What is the probability of students above GRE 325 score?
What is the GRE score middle 50% students?
What is the TOEFL score of top 10% students?
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

X = 107.18 + 6.08 * 1.282

X= 114.97

Hence , TOEFL score of top 10% students is 114.97

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

X = 8.5764 + 0.6048 * 1.282

X= 9.35

Hence CGPA of top 10% students is 9.35

orchestra answered 1 year ago

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