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A frozen yogurt stand offers three flavors of frozen yogurt and three different types of toppings. The owner recently surveyed customers about their favorite one-topping flavor combinations. The results are shown in the two-way relative frequency table below.

| Topping | Vanilla | Chocolate | Strawberry | Total |
|------------|---------|-----------|-------------|-------|
| Sprinkles | 0.10 | 0.15 | 0.05 | 0.30 |
| Nuts | 0.08 | 0.13 | 0.05 | 0.26 |
| Fruit | 0.14 | 0.19 | 0.11 | 0.44 |
| Total | 0.32 | 0.47 | 0.21 | 1.00 |

The owner wants to launch a new product that includes a topping already mixed into the frozen yogurt. If he uses vanilla frozen yogurt as the base of his new mix, which statement is true?

A. The owner should use fruit as the mixed-in topping.
B. The survey results do not show a preference for any of the three topping choices.
C. The owner should use nuts as the mixed-in topping.
D. The owner should use sprinkles as the mixed-in topping.



Answer :

GinnyAnswer
To determine which topping the owner should use for the new vanilla frozen yogurt mix, we need to consider the survey results specifically for the vanilla flavor. Here is the table extracted for vanilla:

[tex]\[ \begin{array}{|r|c|} \hline & \text{Vanilla} \\ \hline \text{Sprinkles} & 0.10 \\ \hline \text{Nuts} & 0.08 \\ \hline \text{Fruit} & 0.14 \\ \hline \end{array} \][/tex]

The task is to identify which topping has the highest relative frequency for the vanilla frozen yogurt. Let's compare the relative frequencies:

- Sprinkles: 0.10
- Nuts: 0.08
- Fruit: 0.14

Based on these relative frequencies, we can see that the topping with the highest relative frequency for vanilla is fruit, with a frequency of 0.14.

Thus, the correct answer is:

A. The owner should use fruit as the mixed-in topping.

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