Question 9
1 pts
Scores on a certain standardized exam follow a $N(\mu=125, \sigma=15)$ distribution. Brittany scored a 149 on the exam.
Compute her Z-score. Round to 2 decimal places as needed.
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Answer
Final Answer: The Z-score for Brittany's score is \(\boxed{1.6}\)
Step 1 ：The Z-score is a measure of how many standard deviations an element is from the mean. To find the Z-score, we subtract the mean from the element and then divide by the standard deviation. In this case, the element is Brittany's score (149), the mean is 125, and the standard deviation is 15.
Step 2 ：Subtract the mean from Brittany's score: \(149 - 125 = 24\)
Step 3 ：Divide the result by the standard deviation: \(\frac{24}{15} = 1.6\)
Step 4 ：The result makes sense. A Z-score of 1.6 means that Brittany's score is 1.6 standard deviations above the mean. This is consistent with the fact that her score of 149 is higher than the mean of 125.
Step 5 ：Final Answer: The Z-score for Brittany's score is \(\boxed{1.6}\)
