2. The grade point averages (GPAs) of a large population of college students are

Question

2. The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.4 and standard deviation.8 (a) What fraction of the students will possess GPA in excess of 3.0? (3 (b) Suppose that the drop out rate of a college is approximately 25%, what points) is (approximately) the lowest GPA that a student has to possess so as to stay in the college? (3 points) (c) Suppose that three students are randomly selected from the student body. What is the probability that all three will possess a GPA in excess of 3.0? (2 points)

Explanation / Answer

a)

probability that student possess GPA in excess of 3.0:

b)

for 25th percentile z score =-0.6745

therfore coresponding cutoff score =mean +z*std deviation =2.4-0.6745*0.8 =1.86

c)

P(all 3 posses a GPA in excess of 3) =(0.2266)3 =0.0116

for normal distribution z score =(X-)/ here mean=       = 2.4 std deviation   == 0.800

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