The manager of a juice bar polled 56 random customers to get feedback on a new smoothie. The results are shown in the frequency table.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Like & Dislike & Total \\
\hline
Adult & 23 & 6 & 29 \\
\hline
Child & 18 & 9 & 27 \\
\hline
Total & 41 & 15 & 56 \\
\hline
\end{tabular}

Complete the statements using the table.

1. The number of children who disliked the smoothie is [tex]$\square$[/tex]

2. The total number of children is [tex]$\square$[/tex]

3. The conditional relative frequency that a customer disliked the new smoothie, given that the person is a child, is approximately [tex]$\square$[/tex]



Answer :

Let's analyze the data provided in the frequency table and fill in the blanks.

1. The number of children who disliked the smoothie:
From the table, we see that among the children, 9 disliked the smoothie. Therefore, the number of children who disliked the smoothie is:
[tex]\[ 9 \][/tex]

2. The total number of children:
The table shows that there are a total of 27 children surveyed. Therefore, the total number of children is:
[tex]\[ 27 \][/tex]

3. The conditional relative frequency that a customer disliked the new smoothie, given that the person is a child:
This is calculated by dividing the number of children who disliked the smoothie by the total number of children. From the table:
[tex]\[ \text{Conditional Relative Frequency} = \frac{\text{Number of children who disliked}}{\text{Total number of children}} = \frac{9}{27} \][/tex]
Simplifying this fraction, we get:
[tex]\[ \frac{9}{27} = \frac{1}{3} \approx 0.3333 \][/tex]

Therefore, the statements can be completed as:
- The number of children who disliked the smoothie is [tex]\( 9 \)[/tex].
- The total number of children is [tex]\( 27 \)[/tex].
- The conditional relative frequency that a customer disliked the new smoothie, given that the person is a child is approximately [tex]\( 0.3333 \)[/tex].