Calculate the standard score of the given $X$ value, $X=40$, where $\mu=36.3$ and $\sigma=39.8$. Round your answer to two decimal places.
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Answer
Rounding to two decimal places, we find that the standard score of the given $X$ value is approximately \(\boxed{0.09}\).
Step 1 ：We are given a value from the dataset, $X=40$, the mean of the dataset, $\mu=36.3$, and the standard deviation of the dataset, $\sigma=39.8$.
Step 2 ：We are asked to calculate the standard score (also known as a z-score), which is a measure of how many standard deviations an element is from the mean.
Step 3 ：The formula to calculate the standard score is $Z = \frac{X - \mu}{\sigma}$.
Step 4 ：Substituting the given values into the formula, we get $Z = \frac{40 - 36.3}{39.8}$.
Step 5 ：Solving the equation, we find that $Z = 0.0929648241206031$.
Step 6 ：Rounding to two decimal places, we find that the standard score of the given $X$ value is approximately \(\boxed{0.09}\).
