Over the last three semesters, the grades on the first test were: Grade Frequenc
ID: 3256188 • Letter: O
Question
Over the last three semesters, the grades on the first test were:
Grade
Frequency
A
27
B
34
C
18
D
3
F
18
Total
100
a. (1) Based on the information above, what is the probability of a student earning a B on the first test this semester? (2) What is the probability of a student earning a C or better on the first test this semester? (3) What approach to assigning probability did you use to make these estimates?
b. Consider the following statement: There are 8 teams in a baseball league. The chances of any team finishing first are one in eight. What approach to assigning probability was used to make this estimate?
c. Consider the following statement: It is now February, and my family has planned an outdoor party on June 25. I believe there is an 80% probability of good weather that day. What approach to assigning probability did I use to make this estimate?
d. Back to the table above. Are the classes A, B, C, D, and F mutually exclusive? Are they collectively exhaustive? If the probabilities associated with each outcome were totaled, what would that total be?
e. State the law of large numbers and explain what it tells us about how big a sample should be taken.
f. What is the random variable in the table above? Is it discrete or continuous?
Grade
Frequency
A
27
B
34
C
18
D
3
F
18
Total
100
Explanation / Answer
(a)
(i)
P(getting a B in first test) = 34/100 = 0.34
(ii)
P(getting a C or better in first test) = (18+34+27)/100 = 0.79
(iii)
We used the method of relative frequencies.
(b)
Classical (axiomatic) approach was used, which means that each team has same probability.
(c)
Subjective approach is used here.
(d)
Yes, the classes are mutually exclusive and collectively exhaustive, which means that the sum of al probabilities will equal one.
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