Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day,  out of every  bottles of nail polish in the company's factory are Soft Lilac. That day, the inventory manager took a sample of bottles of nail polish in the factory. She found that  of the  bottles that she sampled were Soft Lilac.

For the inventory manager's sample, find and write with proper notation the sample proportion and population proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.

(a)	Sample proportion:	▼(Choose one)
(b)	Population proportion:	▼(Choose one)

To solve this problem, we need to determine both the **sample proportion** and the **population proportion** of bottles that were Soft Lilac, based on the data provided.

### Step 1: **Sample Proportion** \( \hat{p} \)

The sample proportion is the ratio of the number of Soft Lilac bottles in the sample to the total number of bottles in the sample.

Let:
- \( x \) be the number of Soft Lilac bottles found in the sample.
- \( n \) be the total number of bottles in the sample.

The formula for the sample proportion \( \hat{p} \) is:
\[
\hat{p} = \frac{x}{n}
\]

From the problem, you mentioned that \( x \) of the \( n \) bottles sampled were Soft Lilac. Let’s use those values to calculate \( \hat{p} \) (if those numbers are missing, please provide them, or I'll assume variables in their place).

### Step 2: **Population Proportion** \( p \)

The population proportion represents the ratio of Soft Lilac bottles in the entire factory.

Let:
- \( k \) be the number of Soft Lilac bottles in the population.
- \( N \) be the total number of bottles in the population.

The population proportion is given by:
\[
p = \frac{k}{N}
\]

You mentioned that out of every \( N \) bottles in the factory, \( k \) are Soft Lilac. Using these numbers, we can compute the population proportion \( p \) (again, if the values are missing, please provide them).

### Conclusion:

(a) **Sample Proportion** \( \hat{p} = \frac{x}{n} \)

(b) **Population Proportion** \( p = \frac{k}{N} \)

Please fill in the specific numbers for \( x \), \( n \), \( k \), and \( N \), and I'll finalize the calculation.

Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day, out of every bottles of nail polish in the company's factory are Soft Lilac. That day, the inventory manager took a sample of bottles of nail polish in the factory. She found that of the bottles that she sampled were Soft Lilac. For the inventory manager's sample, find and write with proper notation the sample proportion and population proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.

Learn how to calculate the sample and population proportion of Soft Lilac nail polish bottles in Zahra's factory. This statistics problem covers key concepts like sample proportion and population proportion using real-world data. Suitable for students in Grades 9-12.

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