Question

zahra is a company specializing in high - end cosmetics. its signature nail polish color is soft lilac. on a certain day, the companys factory had 7400 bottles of nail polish, and 1800 of those bottles were soft lilac. on that day, the inventory manager took a sample of 33 bottles of nail polish in the factory. she found that 6 of those bottles were soft lilac. for the inventory managers 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: select = (b) population proportion: select =

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}$ is calculated as the number of successes in the sample divided by the sample size. Here, the number of Soft - Lilac bottles in the sample is 6 and the sample size $n = 33$. So, $\hat{p}=\frac{6}{33}\approx0.18$.

Step2: Calculate population proportion

The population proportion $p$ is calculated as the number of successes in the population divided by the population size. The number of Soft - Lilac bottles in the population is 1800 and the population size $N = 7400$. So, $p=\frac{1800}{7400}\approx0.24$.

Answer:

(a) $\hat{p}=0.18$
(b) $p = 0.24$