Question

This Excel file Undergrad Survey shows the data resulting from a survey of 50 undergraduate students at Clemson University. Majors of students in the survey are accounting (A), economics and finance (EF), management (M), marketing (MR), computer information systems (IS), other (O), and undecided (UN). "Number of affiliations" is the number of social networking sites at which the student is registered; "Spending" is the amount spent on textbooks for the current semester. The other variables are self-explanatory.

We will assume that this sample is a representative sample of all Clemson undergraduates. Use Excel or statcrunch to make a histogram of GPA to verify that the distribution of GPA can be approximated by the N(3.12, 0.4) normal model.

Question 1. The School of Business at Clemson has created a rigorous new International Business Studies major to better prepare their students for the global marketplace. A GPA of 3.69 or higher is required for a Clemson undergraduate to change his/her major to International Business Studies. What is the probability that a randomly selected Clemson undergraduate has a GPA of at least 3.69? (Use 4 decimal places in your answer).

Question 2. To attract high-quality current Clemson undergraduates into the new International Business Studies major, scholarships in International Business Studies will be offered to a Clemson undergraduate if his/her GPA is at or above the 95.54th percentile. What is the minimum GPA required to meet this criterion?

The GPA Values:

2.38
2.42
2.45
2.50
2.60
2.61
2.65
2.67
2.74
2.75
2.75
2.76
2.80
2.87
2.88
2.91
2.92
2.93
2.94
3.00
3.02
3.09
3.10
3.11
3.13
3.14
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.26
3.28
3.33
3.34
3.43
3.44
3.48
3.50
3.55
3.62
3.62
3.63
3.71
3.72
3.77
3.85
4.00

Answer 1

Question 1:

Here total number of students GPA is given = 50

Number of people who have GPA more than 3.69 = 5

Therefore,

Pr(That a student has GPA more than 3.69) = 5/50 = 0.1

Here X ~ NORMAL (3.12, 0.4)

so Pr(X > 3.69) = Pr(X > 3.69 ; 3.12 ; 0.4)

Z = (3.69 - 3.12)/ 0.4 = 1.425

Pr(X > 3.69) = Pr(X > 3.69 ; 3.12 ; 0.4) = 1 - Pr(Z < 1.425) = 1 - 0.9229 = 0.0771

Question 2

Here GPA would be above 95.54th percentile

so as per Z table relative to that percentile is = 1.70

so Z = (X - 3.12)/ 0.4 = 1.70

X = 3.12 + 0.4 * 1.70 = 3.80

so any person with GPA above or equal to 3.80 is eligible for that.