95% of data under a normal distribution curve fall between which z-scores?

Question

BlackTom AI · Accepted Answer

To tackle this question, I’ll compare each option against the typical empirical rule for the normal distribution and the corresponding z-score intervals.
Option A: –1 and +1. This interval captures about 68% of the data under a normal curve. Since the question asks for 95% coverage, this option underestimates the spread and is not correct for 95%.
Option B: –2 and +2. This interval is commonly associated with capturing roughly 95% of the data in a standard normal distribution, aligning with the well-known 68-95-99.7 rule (empirical rule). While the exact figure is sometimes cited as 95% or 95.44%, this range is the standard approximation used for 95% coverage, making it the most suitable option.
Option C: –2.5 and +2.5. Extending to ±2.5 would capture more data than ±2, and typically corresponds to about 99% of the data, not 95%. This overestimates the required proportion for the stated question.
Option D: –3 and +3. The ±3 range encompasses about 99.7% of the data, far exceeding 95%. This would be used for near-complete coverage of the distribution rather than the 95% target.
In summary, the options reflect increasing intervals around zero with progressively larger portions of the distribution, and Option B best matches the conventional 95% interval for a normal distribution. The other choices either understate or overstate the portion of data captured by the interval.

95% of data under a normal distribution curve fall between which z-scores?单项选择题

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