Question:
A study had a normal distribution with the median value as 200 and standard deviation 20. 68% of values will fall between:
A study had a normal distribution with the median value as 200 and standard deviation 20. 68% of values will fall between:
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68% of values lie within one standard deviation of the mean in a normal curve.
Updated On: Jun 23, 2026
- 160-240
- 170-230
- 180-220
- 190-210
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The Correct Option is C
Solution and Explanation
Step 1: In a normal (Gaussian) distribution, the mean, median, and mode are all equal. So the mean here is also 200.
Step 2: The empirical rule states that about 68% of values lie within \(\pm 1\) standard deviation of the mean.
Step 3: Compute the interval: \(200 \pm 1 \times 20 = 180\) to \(220\). So 68% of the data fall between 180 and 220.
For reference: 95% would lie within \(\pm 2\) SD, i.e. \(200 \pm 40 = 160\) to \(240\) (option a), and 99.7% within \(\pm 3\) SD.
Ref: Park's PSM, 24th ed., Page 885.
Step 2: The empirical rule states that about 68% of values lie within \(\pm 1\) standard deviation of the mean.
Step 3: Compute the interval: \(200 \pm 1 \times 20 = 180\) to \(220\). So 68% of the data fall between 180 and 220.
For reference: 95% would lie within \(\pm 2\) SD, i.e. \(200 \pm 40 = 160\) to \(240\) (option a), and 99.7% within \(\pm 3\) SD.
Ref: Park's PSM, 24th ed., Page 885.
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