Let's analyze the problem step by step and fill in the values for the cells labeled [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
The given table contains the results of a poll regarding the ownership of cell phones and laptops among 300 people. Here is the table again for reference:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Cell Phone & No Cell Phone & Total \\
\hline
Laptop & 82 & 11 & b \\
\hline
No Laptop & 159 & a & 207 \\
\hline
Total & 241 & 59 & 300 \\
\hline
\end{tabular}
\][/tex]
### Calculation of cell labeled [tex]\( a \)[/tex]:
To determine the value for the cell [tex]\( a \)[/tex] (No Cell Phone & No Laptop):
1. We know that the total number of people who do not have laptops is 207.
2. Out of these 207 people, 159 people have cell phones.
3. Therefore, the number of people who do not have a cell phone and do not have a laptop can be calculated as:
[tex]\[
a = \text{Total No Laptop} - \text{No Laptop with Cell Phone}
\][/tex]
[tex]\[
a = 207 - 48 = 159
\][/tex]
Hence, the cell labeled [tex]\( a \)[/tex] is [tex]\( 159 \)[/tex].
### Calculation of cell labeled [tex]\( b \)[/tex]:
To determine the value for the cell [tex]\( b \)[/tex] (Laptop Total):
1. We know that 82 people have both a laptop and a cell phone.
2. Additionally, 11 people have a laptop but do not have a cell phone.
3. Therefore, the total number of people who have laptops can be calculated by adding these two numbers:
[tex]\[
b = \text{Laptop with Cell Phone} + \text{Laptop without Cell Phone}
\][/tex]
[tex]\[
b = 82 + 11 = 93
\][/tex]
Hence, the cell labeled [tex]\( b \)[/tex] is [tex]\( 93 \)[/tex].
### Final statements:
- The cell labeled [tex]\( a \)[/tex] is [tex]\( \boxed{159} \)[/tex].
- The cell labeled [tex]\( b \)[/tex] is [tex]\( \boxed{93} \)[/tex].
