Question:easy
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
Read this off the empirical (68-95-99.7) rule. For a bell-shaped curve, the percentage of data captured depends only on how many SDs you move out from the centre: $\pm 1$ SD holds $68\%$, $\pm 2$ SD holds $95\%$, and $\pm 3$ SD holds $99.7\%$.
First fix the centre. Because the curve is normal, mean = median = mode = $200$. The SD is $20$.
The question asks for $68\%$, so move out exactly one SD on each side: $200 - 20 = 180$ and $200 + 20 = 220$. The band is $180$ to $220$, which is option $c$.
Spot the traps: $160$ to $240$ is the $\pm 2$ SD ($95\%$) band, $190$ to $210$ is only $\pm 0.5$ SD, and $170$ to $230$ does not match any clean SD multiple.
Ref: Park's PSM, 24th ed., p. 885.
First fix the centre. Because the curve is normal, mean = median = mode = $200$. The SD is $20$.
The question asks for $68\%$, so move out exactly one SD on each side: $200 - 20 = 180$ and $200 + 20 = 220$. The band is $180$ to $220$, which is option $c$.
Spot the traps: $160$ to $240$ is the $\pm 2$ SD ($95\%$) band, $190$ to $210$ is only $\pm 0.5$ SD, and $170$ to $230$ does not match any clean SD multiple.
Ref: Park's PSM, 24th ed., p. 885.
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