alleryStart learning →The z-scores minus 2 and plus 2 correspond to which pair of original values in a distribution with mean 50 and deviation 6?
A48 and 52
B32 and 68
C38 and 62
D44 and 56
Answer & Solution
Correct answer: C. 38 and 62
1. A z-score of plus 2 means two standard deviations above the mean.
2. The z-scores are minus 1 and plus 1 for 44 and 56 respectively, which fixes the deviation at 6.
3. The z-scores are minus 2 and plus 2 for 38 and 62 respectively.
4. 44 and 56 are the one-deviation pair, which makes them the trap here.
5. Three deviations would give 32 and 68.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_
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