Question 10, 8.2.03
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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.
$\overset{―}{x} = 25, n = 36, σ = 2, confidence level = 95 %$

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 $◻$ to $◻$
(Type integers or decimals rounded to one decimal place as needed.)

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So, the final answer is: The confidence interval is from $24.3$ to $25.7$ .

Steps

Step 1 ：Given values are sample mean $\overset{―}{x} = 25$ , sample size $n = 36$ , population standard deviation $σ = 2$ , 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 $z \cdot \frac{σ}{\sqrt{n}}$ . 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 $\overset{―}{x} \pm$ 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 $24.3$ to $25.7$ .

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