Let's break down the calculation for the 95% confidence interval for a proportion, given the summary statistics: - **mean (p̂):** 0.1518 - **sd:** 0.0244 - **n:** 10,000 ### Step 1: Formula for Confidence Interval For a proportion, the 95% confidence interval is: \[ \text{CI} = \hat{p} \pm z^* \times \frac{sd}{\sqrt{n}} \] But since the mean and sd are provided from the sample, and n is large, we can use: \[ \text{CI} = \hat{p} \pm z^* \times sd \] For 95% confidence, \( z^* = 1.96 \). ### Step 2: Plug in the Values \[ \text{Lower bound} = 0.1518 - 1.96 \times 0.0244 \] \[ \text{Upper bound} = 0.1518 + 1.96 \times 0.0244 \] ### Step 3: Calculation - \( 1.96 \times 0.0244 = 0.047824 \) So, - **Lower bound:** \( 0.1518 - 0.047824 = 0.103976 \) - **Upper bound:** \( 0.1518 + 0.047824 = 0.199624 \) ### Step 4: Round to Four Decimal Places - **Lower bound:** 0.1040 - **Upper bound:** 0.1996 --- **Final Answer:** \[ \boxed{0.1040,\ 0.1996} \]