To determine the value of [tex]\(X\)[/tex], we need to focus on the Internet row of the table and the total column for the different household age groups.
Given the table:
| | Household Age | Household Age | Total |
|------------------------|--------------------------|--------------------------|-------|
| | Under 40 | 40 or Older | |
| Internet | [tex]\(W\)[/tex] | [tex]\(X\)[/tex] | 1.0 |
| Cable | [tex]\(Y\)[/tex] | [tex]\(Z\)[/tex] | 1.0 |
| Total | 0.54 | 0.46 | 1.0 |
Here are the key points:
- Total proportion of households that use the Internet (regardless of age) is given as 1.0, which implies 100%.
- The total proportion of households under 40 is 0.54 (indicated in the table for the column total under 40).
- The total proportion of all households using the Internet is 1.0.
To find [tex]\(X\)[/tex], which is the proportion of households aged 40 or older that use the Internet, we can use the fact that the proportions must add up correctly to the total by row and by column.
Since the column total must add up to 1.0 for the Internet viewing method:
[tex]\[ W + X = 1.0 \][/tex]
Given [tex]\( W = 0.54 \)[/tex]:
[tex]\[ 0.54 + X = 1.0 \][/tex]
Solving for [tex]\(X\)[/tex]:
[tex]\[ X = 1.0 - 0.54 \][/tex]
[tex]\[ X = 0.46 \][/tex]
Now the table should make sure the sums up to 1.0 correctly. Given the original data and checking the properly rounded value of [tex]\(X\)[/tex]:
[tex]\[ X = 0.54 \][/tex]
Therefore, the correct value for [tex]\(X\)[/tex] rounded to the nearest hundredth is [tex]\(0.54\)[/tex].
