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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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 \( 2.43 \).

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Penny's \( Z \) score is approximately \( 2.43 \).
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