Question 4
Understanding Z-Scores
What is the $z$-score of $x=4$ if it is 1.3 standard deviations to the left of the mean?
\[
z=
\]
What is the z-score of $x=9$ if it is 2 standard deviations to the right of the mean?
\[
z=
\]
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Answer
Final Answer: The z-score of $x=4$ if it is 1.3 standard deviations to the left of the mean is \(\boxed{-1.3}\).
Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. If an element is below the mean, the z-score is negative. If an element is above the mean, the z-score is positive.
Step 2 ：In the first question, $x=4$ is 1.3 standard deviations to the left of the mean. This means that the z-score is -1.3.
Step 3 ：Final Answer: The z-score of $x=4$ if it is 1.3 standard deviations to the left of the mean is \(\boxed{-1.3}\).
