Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
\[
\mu=24 \text { and } \sigma=7 ; n=71 ; \bar{x}=23
\]

Answer 5 Points
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Keyboard Shortc

Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. To calculate the z-score for a sample mean, we can use the formula: \(z = \frac{{\bar{x} - \mu}}{{\sigma / \sqrt{n}}}\) where: \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.

Step 2 ：In this case, we have \(\mu = 24\), \(\sigma = 7\), \(n = 71\), and \(\bar{x} = 23\). We can substitute these values into the formula to find the z-score.

Step 3 ：Substituting the given values into the formula, we get \(z = \frac{{23 - 24}}{{7 / \sqrt{71}}}\).

Step 4 ：Calculating the above expression, we get \(z = -1.203735681882337\).

Step 5 ：The question asks for the answer to be rounded to two decimal places. Therefore, we need to round this result to two decimal places.

Step 6 ：Rounding the z-score to two decimal places, we get \(z = -1.2\).

Step 7 ：Final Answer: The standard score (z-score) of the given sample mean, rounded to two decimal places, is \(\boxed{-1.2}\).