According to a 2009 Reader's Digest article, people throw away approximately $12 \%$ of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 58 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.06 and 0.14 ? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Step 1 ：Given that the population proportion (p) is 0.12 and the sample size (n) is 58.

Step 2 ：We are looking for the probability that the sample proportion (p̂) is between 0.06 and 0.14.

Step 3 ：We first calculate the standard deviation of the sample proportion using the formula \(\sqrt{p(1-p)/n}\), which gives us approximately 0.0427.

Step 4 ：We then calculate the z-scores for 0.06 and 0.14 using the formula \(z = (x - μ) / σ\), where x is the value from the sample, μ is the population mean, and σ is the standard deviation. This gives us approximately -1.4062 and 0.4687 respectively.

Step 5 ：We use a z-table to find the probabilities associated with these z-scores, which are approximately 0.0798 and 0.6804 respectively.

Step 6 ：We subtract the smaller probability from the larger one to find the probability that the sample proportion is between 0.06 and 0.14, which gives us approximately 0.6005.

Step 7 ：Final Answer: The probability that the sample proportion is between 0.06 and 0.14 is approximately \(\boxed{0.6005}\).