Construct a relative frequency marginal distribution for the given contingency t
ID: 3218085 • Letter: C
Question
Construct a relative frequency marginal distribution for the given contingency table. Round valuese to the nearest thousandth.
x1
x2
x3
y1
20
25
10
y2
40
35
35
Construct a conditional distribution by x for the given contingency table. Round valuese to the nearest thousandth.
x1
x2
x3
y1
30
40
20
y2
50
65
65
The managers of a corporation were surveyed to determine the background that leads to a successful manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below. Given that a manager is only a fair manager, what is the probability that this manager has no college background? Educational Background
manager rating
H.S Degree
Some College
College Degree
Master's or Ph.D
Total
Good Fair Poor
1
5
24
3
39
9
13
45
20
87
6
2
4
22
34
Totals
22
20
73
45
160
4) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack, a three, a club or a diamond. Round to the nearest hundredth.
5) At Bill's community college, 49.2% of students are Caucasian and 4.1% of students are Caucasian math majors. What percentage of Caucasian students are math majors?
x1
x2
x3
y1
20
25
10
y2
40
35
35
Explanation / Answer
Construct a relative frequency marginal distribution for the given contingency table
Marginal distribution of X and Y is,
f(x) = f(x,y) summation over y
f(y) = f(x,y) summation over x
Relative frequency is defined as,
relative frequency = count / total count
Marginal distribution of X is,
Marginal distribution of Y is,
The managers of a corporation were surveyed to determine the background that leads to a successful manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below. Given that a manager is only a fair manager, what is the probability that this manager has no college background?
Here we have to find P(no college degree / fair manager) .
P(no college degree / fair manager) = P(no college degree and fair manager) / P(fair manager)
P(no college degree / fair manager) = 9/160
P(fair manager) = 87/160
P(no college degree / fair manager) = (9/160) / (87/160)
= 9/87
4) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack, a three, a club or a diamond.
P(getiing a jack, a three, a club or a diamond) =
By using generalization of addition theorem,
P(getiing a jack, a three, a club or a diamond) = P(a jack) + P(a three) + P(a club) + P(a diamond)
There are 4 jacks, 4 three's, 13 clubs, and 13 diamonds in the standard deck.
P(getiing a jack, a three, a club or a diamond) = 4/52 + 4/52 + 13/52 + 13/52
= 34/52
5) At Bill's community college, 49.2% of students are Caucasian and 4.1% of students are Caucasian math majors. What percentage of Caucasian students are math majors?
Here we have given that,
P( Caucasian) = 49.2% = 0.492
P( Caucasian math majors) = 4.1% = 0.041
And we have to find P(math majors).
Here math major and Caucasian are independent event.
So the definition of independent event is,
If A and B are two events then they are said to be independent iff P(A and B) = P(A) * P(B)
Here we use same definition.
P(Caucasian math majors) = P(Caucasian) * P(math majors)
0.041 = 0.492 * P(math majors)
P(math major) = 0.041/0.492 = 0.0833 = 8.3%
x1 x2 x3 total y1 20 25 10 55 y2 40 35 35 110 total 60 60 45 165