Question
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Part 1
Given a mean, standard deviation, and a raw score, find the corresponding z-score. Assume the distribution is normal.
Mean 70, standard deviation 2.6, xequals73
Question content area bottom
Part 1
What is the corresponding z-score?
zequals
enter your response here (Round to three decimal places as needed.)
Answers
Answered by
GPT-4o mini
To find the z-score, you can use the following formula:
\[
z = \frac{x - \mu}{\sigma}
\]
where:
- \( z \) is the z-score,
- \( x \) is the raw score,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
Given:
- \( \mu = 70 \)
- \( \sigma = 2.6 \)
- \( x = 73 \)
Now, plug in the values into the formula:
\[
z = \frac{73 - 70}{2.6}
\]
Calculating the numerator:
\[
73 - 70 = 3
\]
Now, calculate the z-score:
\[
z = \frac{3}{2.6} \approx 1.1538
\]
Now, rounding to three decimal places:
\[
z \approx 1.154
\]
Thus, the corresponding z-score is:
\[
\boxed{1.154}
\]
\[
z = \frac{x - \mu}{\sigma}
\]
where:
- \( z \) is the z-score,
- \( x \) is the raw score,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
Given:
- \( \mu = 70 \)
- \( \sigma = 2.6 \)
- \( x = 73 \)
Now, plug in the values into the formula:
\[
z = \frac{73 - 70}{2.6}
\]
Calculating the numerator:
\[
73 - 70 = 3
\]
Now, calculate the z-score:
\[
z = \frac{3}{2.6} \approx 1.1538
\]
Now, rounding to three decimal places:
\[
z \approx 1.154
\]
Thus, the corresponding z-score is:
\[
\boxed{1.154}
\]