During the first year at a university that uses a four-point grading system, a freshman took ten three-credit courses and received two As, three Bs, four Cs, and one D.
a) Compute this student's g.p.a.
What I did : 2+3+4+1/4=2.5
2.5 g.p.a
b) Let the random variable X denote the number of points corresponding to a given letter grade. Find the probability distribution of the random variable X and compute E(X), the expected value of X.
I set up a probability distribution table to help me :
X A/4 B/3 C/2 D/1
P(x=x) 2 3 4 1
then I did this:
2/10 =.2, 3/10 =.3, 4/10=.4, 1/10=.1
then :
(4) * (.2) + (3) * (.3) + (2) * (.4)+ (1) (.1) = .8+.9+.8+.1=2.6
E(X) = 2.6
a) Compute this student's g.p.a.
What ::::YOU:::: did : 2+3+4+1/4=2.5
2.5 g.p.a
==========================
What :::: I :::: did
took TEN, each with a number and a value
[2*4 + 3*3 + 4*2 + 1*1 ] / 10
[ 8 + 9 +8 + 1 ] / 10
26/10
2.6
Note ---- That is what you got for part B. That was not a coincidence.
a) The calculation for GPA is incorrect. To calculate GPA, you need to consider the grade points associated with each letter grade. In a four-point grading system, typically:
A = 4
B = 3
C = 2
D = 1
So, using the given information - two As, three Bs, four Cs, and one D - you can calculate the GPA as follows:
Total grade points = (2 * 4) + (3 * 3) + (4 * 2) + (1 * 1) = 8 + 9 + 8 + 1 = 26
Total credits = 10 * 3 = 30
GPA = Total grade points / Total credits = 26 / 30 = 0.8667 (rounded to four decimal places)
Therefore, the student's GPA is approximately 0.8667.
b) The probability distribution for the random variable X (denoting the number of points corresponding to a given letter grade) can be calculated using the given information:
X | P(X)
--------------
A/4 | 2/10
B/3 | 3/10
C/2 | 4/10
D/1 | 1/10
To find the expected value (E(X)), you multiply each value of X by its corresponding probability and sum them up. Using the probability distribution:
E(X) = (A/4) * (2/10) + (B/3) * (3/10) + (C/2) * (4/10) + (D/1) * (1/10)
= (1/2) + (3/10) + (4/10) + (1/10)
= 1/2 + 3/10 + 4/10 + 1/10
= 5/10 + 3/10 + 4/10 + 1/10
= 13/10
= 1.3
Therefore, the expected value (E(X)) of the random variable X is 1.3.
To compute the student's GPA, you need to calculate the weighted average of the grade points for each course. In a four-point grading system, typically the grades A, B, C, and D correspond to 4, 3, 2, and 1 grade points, respectively. Here's how you can calculate the GPA:
1. Calculate the total grade points earned:
- 2 As * 4 grade points = 8 grade points
- 3 Bs * 3 grade points = 9 grade points
- 4 Cs * 2 grade points = 8 grade points
- 1 D * 1 grade point = 1 grade point
Total grade points = 8 + 9 + 8 + 1 = 26 grade points
2. Calculate the total credit hours taken:
- 10 courses * 3 credit hours per course = 30 credit hours
3. Divide the total grade points by the total credit hours:
GPA = Total grade points / Total credit hours = 26 grade points / 30 credit hours = 0.8667
Therefore, the student's GPA is approximately 0.8667 or about 0.87.
For calculating the probability distribution of the random variable X and finding the expected value E(X), your approach is correct. You set up a probability distribution table, assigning probabilities to each letter grade based on their occurrences. Here's how you can calculate E(X):
1. Assign probabilities to each letter grade based on their occurrences (as you have done):
- P(A) = 2/10 = 0.2
- P(B) = 3/10 = 0.3
- P(C) = 4/10 = 0.4
- P(D) = 1/10 = 0.1
2. Calculate E(X) by taking the sum of the products of each letter grade and its corresponding probability:
E(X) = (4 * 0.2) + (3 * 0.3) + (2 * 0.4) + (1 * 0.1) = 2.6
Therefore, the expected value of X is 2.6.