I assumed that 3 households are sampled.
Now, is the number in each of these households equal to 1, 3 and 8 people?
Next, the question says, samples of n=2 are randomly selected (with replacement) from these 3.
So are sample space is
11
13
31
33
18
81
38
88
83
88
This is done 9 times.
Is that how you understand the problem?
When they select the household with only 1 person, the variance is 0
When they select the household with 8 people, they variance will be from a discrete uniform distribution
Similarly for household with 3 individuals.
Which situation could best be represented by the integer 120?
1. could be negative but the likely of losing 120 pounds is very low
2. this number would be positive
3. could be between -1 to - infinity
answer: 3. the number of feet below a surface
SOLUTION
We will use the formula

Applying we have

Now using a Zscore calculator for 1.370320, we have
P(xHence the answer is 0.9147
Remark
The best way to answer something like this is to actually graph both equations. I have done that for you below.
Red Line: f(x) = 1/4x - 1
Blue Line: g(x) = 1/2x - 2
Now look at the answers.
A: The first one is incorrect. You don't need the graph to tell you that. The larger the number in front of the x, the steeper the line. Put another way, the larger the slope, the steeper the line. The y intercept is lower however.
B is wrong. g(x) is steeper, but the y intercept is lower not higher than f(x) [Negatives do strange things].
C:The g(x) is steeper (we've said that a couple of times), and it has a lower y intercept.
D is correct.
E is just wrong. Both parts are incorrect.