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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|}
\hline & 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 :

GinnyAnswer
Sure, let's work through the information given in the problem step by step:

1. Identifying the number of children who disliked the smoothie:

According to the table, the number of children who disliked the smoothie is explicitly provided.

- The number of children who disliked the smoothie is: 9

2. Identifying the total number of children:

The table also provides the total number of children.

- The total number of children is: 27

3. Calculating the conditional relative frequency that a customer disliked the new smoothie, given that the person is a child:

The conditional relative frequency is calculated as the ratio of the number of children who disliked the smoothie to the total number of children.

- Number of children who disliked the smoothie: 9
- Total number of children: 27
- Formula for the conditional relative frequency:

[tex]\[ \text{Conditional Relative Frequency} = \frac{\text{Number of children who disliked the smoothie}}{\text{Total number of children}} \][/tex]

Substituting the values:

[tex]\[ \text{Conditional Relative Frequency} = \frac{9}{27} \][/tex]

Simplifying the fraction:

[tex]\[ \text{Conditional Relative Frequency} \approx 0.3333 \][/tex]

Hence, the completed statements are:
- The number of children who disliked the smoothie is: 9
- The total number of children is: 27
- The conditional relative frequency that a customer disliked the new smoothie, given that the person is a child is approximately: 0.3333 or 33.33%

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