Question 10, 8.2.03
Part 1 of 4
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A sample mean, sample size, population standard deviation, and confidence level are provided. Use this informatio to complete parts (a) through (c) below.
\[
\overline{\mathrm{x}}=25, \mathrm{n}=36, \sigma=2 \text {, confidence level }=95 \%
\]

Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
a. Use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.

The confidence interval is from $\square$ to $\square$
(Type integers or decimals rounded to one decimal place as needed.)

Step 1 ：Given values are sample mean \(\overline{x} = 25\), sample size \(n = 36\), population standard deviation \(\sigma = 2\), and confidence level of 95% which corresponds to a z-score of \(z = 1.96\).

Step 2 ：First, calculate the margin of error using the formula \(z \cdot \frac{\sigma}{\sqrt{n}}\). Substituting the given values, we get \(1.96 \cdot \frac{2}{\sqrt{36}} = 0.653\).

Step 3 ：Next, calculate the confidence interval using the formula \(\overline{x} \pm\) margin of error. Substituting the given values, we get \(25 - 0.653 = 24.347\) and \(25 + 0.653 = 25.653\).

Step 4 ：Rounding to one decimal place, the confidence interval is from \(24.3\) to \(25.7\).

Step 5 ：So, the final answer is: The confidence interval is from \(\boxed{24.3}\) to \(\boxed{25.7}\).