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To solve the problem:

### (a) **Sample Proportion**:
The sample proportion is calculated by dividing the number of members with bronze status in the sample by the total number of sampled members.

\[
\hat{p} = \frac{11}{19} \approx 0.579
\]

So, the sample proportion (rounded to two decimal places) is:

\[
\hat{p} = 0.58
\]

### (b) **Population Proportion**:
The population proportion is calculated by dividing the total number of bronze status members in the population by the total number of members in the gym.

\[
p = \frac{330}{560} \approx 0.589
\]

So, the population proportion (rounded to two decimal places) is:

\[
p = 0.59
\]

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Do you need further clarification on this problem or additional details?

Here are 5 related questions for further practice:
1. What is the difference between sample proportion and population proportion?
2. How would increasing the sample size affect the accuracy of the sample proportion?
3. If the population size increased to 700 with 410 bronze members, what would the new population proportion be?
4. What is the margin of error for the sample proportion in this case?
5. How can we use this data to predict the bronze status for future gym members?

**Tip**: When calculating proportions, always make sure to round only at the final step to minimize rounding errors throughout the calculation.

Rock Solid Gym offers several levels of membership status. All customers start at the bronze status. One day, the membership coordinator took a sample of members of the gym. She found that 11 of the 19 members she sampled had bronze status. The gym had 560 members on that day, and 330 of these members had bronze status. Find the sample and population proportion of members who had bronze status, rounded to two decimal places.

Learn how to calculate both the sample and population proportions of gym members who have bronze status. In this problem, we find the sample proportion from 19 members and the population proportion from 560 total members, rounded to two decimal places.

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