A candy bar with a 25-gram label weight is selected at random from a production line
and weighted. Assuming that a candy bar cannot exceed 25 grams in weight, specify the
sample space.

The sample space represents all possible outcomes of an experiment or random process. In this case, the sample space is the set of all possible weights that a randomly selected candy bar can have. Since the candy bar cannot exceed 25 grams in weight, and assuming that it can weigh any value from 0 grams up to and including 25 grams, the sample space can be represented as:

\[ S = \{ x \mid 0 \leq x \leq 25 \} \]

Where \( x \) is the weight of the candy bar in grams.

This means that the sample space \( S \) includes all possible real numbers from 0 grams to 25 grams, inclusive.

Would you like more details or have any questions about this? Here are five related questions to consider:

1. How would the sample space change if the candy bar could exceed 25 grams in weight?
2. What if the weight could only be a whole number (integer) between 0 and 25 grams?
3. How would you describe the probability distribution of the candy bar's weight?
4. If the mean weight of the candy bars is 24 grams, what does that imply about the production process?
5. How would you calculate the probability of selecting a candy bar that weighs exactly 20 grams?

**Tip:** When dealing with continuous sample spaces, it's important to consider the range of possible outcomes carefully, especially whether or not endpoints (like 25 grams) are included.

Explore the sample space of a candy bar's weight, ranging from 0 to 25 grams. Understand how this relates to probability in production lines. Suitable for Grades 10-12.

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