May Bush
06/22/2023 · Primary School
A sample of statistics exams from a university has a mean of 75 and a standard deviation of 7. Penny has scored a 92 on her exam. What is Penny's \( Z \) score in the sample?
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Step-by-step Solution
To calculate Penny's \( Z \) score, we can use the formula for the \( Z \) score:
\[
Z = \frac{(X - \mu)}{\sigma}
\]
where:
- \( X \) is Penny's score,
- \( \mu \) is the mean of the sample,
- \( \sigma \) is the standard deviation of the sample.
Given:
- \( X = 92 \)
- \( \mu = 75 \)
- \( \sigma = 7 \)
Now, we can substitute these values into the formula:
\[
Z = \frac{(92 - 75)}{7}
\]
Calculating the numerator:
\[
92 - 75 = 17
\]
Now, substituting back into the formula:
\[
Z = \frac{17}{7} \approx 2.43
\]
Thus, Penny's \( Z \) score is approximately \( 2.43 \).
Quick Answer
Penny's \( Z \) score is approximately \( 2.43 \).
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