A university posts the grade distributions for its courses online. Students in a class in the fall semester received these grades: 19% A, 7% A−, 6% B+, 16% B, 12% B−, 5% C+, 15% C, 5% C−, 3% D+, 5% D, 4% D−, and 3% F. Choose a student at random. To "choose at random" means to give every student the same chance to be chosen. The student's grade on a four-point scale (with
A = 4,
A− = 3.7,
B+ = 3.3,
B = 3.0,
B− = 2.7,
C+ = 2.3,
C = 2.0,
C− = 1.7,
D+ = 1.3,
D = 1.0,
D− = 0.7,
and
F = 0.0)
is a discrete random variable X with this probability distribution.
Value of X |
0.0 |
0.7 |
1.0 |
1.3 |
1.7 |
2.0 |
2.3 |
2.7 |
3.0 |
3.3 |
3.7 |
4.0 |
Probability |
0.03 |
0.04 |
0.05 |
0.03 |
0.05 |
0.15 |
0.05 |
0.12 |
0.16 |
0.06 |
0.07 |
0.19 |
(a) Say in words what the meaning of P(X ≥ 3.0) is.
proportion of students that got lower than a Dproportion of students that got a B or higher proportion of students that got a D or lowerproportion of students that got less than a Bproportion of students that got A's
What is this probability? (Enter your answer to two decimal places.)
(b) Write the event "the student got a grade poorer than B−" in terms of values of the random variable X.
P(X ≤ 2.7)P(X ≥ 2.7) P(X < 2.7)P(X < 2.0)
What is the probability of this event? (Enter your answer to two decimal places.)