The class mean score on a test was 60, and the standard deviation was 15. If Jack's score was within...
GMAT Number Properties : (NP) Questions
Source: Official Guide
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Post a Query
The class mean score on a test was \(60\), and the standard deviation was \(15\). If Jack's score was within \(2\) standard deviations of the mean, what is the lowest score he could have received?
Solution
- Translate the problem requirements: "Within 2 standard deviations of the mean" means Jack's score falls between \(\mathrm{mean} - 2 \times \mathrm{standard\ deviation}\) and \(\mathrm{mean} + 2 \times \mathrm{standard\ deviation}\). We want the lowest possible score in this range.
- Identify the acceptable score range: Calculate the bounds: lower = \(60 - 2 \times 15 = 30\), upper = \(60 + 2 \times 15 = 90\).
- Determine the minimum score: The lowest score in [30, 90] is 30.
Final Answer
The lowest score Jack could have received while still within 2 standard deviations of the mean is 30 (choice A).
Answer Choices Explained
A
30
B
31
C
45
D
90
E
89
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