Marked out of 1.00 For \( C=95 \% \) If \( \sigma=5.34 \) and \( \mathrm{n}=45 \) then \( E=1.56 \)

To determine if the given information is correct, we can calculate the margin of error \( E \) using the formula for the margin of error in a confidence interval for a population mean: \[ E = z \cdot \frac{\sigma}{\sqrt{n}} \] Where: - \( E \) is the margin of error, - \( z \) is the z-score corresponding to the desired confidence level, - \( \sigma \) is the population standard deviation, - \( n \) is the sample size. ### Step 1: Find the z-score for \( C = 95\% \) For a 95% confidence level, the z-score can be found using standard normal distribution tables or calculators. The z-score for 95% confidence is approximately: \[ z \approx 1.96 \] ### Step 2: Substitute the known values into the formula Given: - \( \sigma = 5.34 \) - \( n = 45 \) We can now calculate \( E \): \[ E = 1.96 \cdot \frac{5.34}{\sqrt{45}} \] ### Step 3: Calculate \( \sqrt{n} \) First, we calculate \( \sqrt{45} \): \[ \sqrt{45} \approx 6.708 \] ### Step 4: Calculate \( \frac{\sigma}{\sqrt{n}} \) Now, we calculate \( \frac{5.34}{\sqrt{45}} \): \[ \frac{5.34}{6.708} \approx 0.796 \] ### Step 5: Calculate the margin of error \( E \) Now we can calculate \( E \): \[ E = 1.96 \cdot 0.796 \approx 1.56 \] ### Conclusion The calculated margin of error \( E \) is approximately 1.56, which matches the given value. Therefore, the information provided is correct.