CA Foundation · Quantitative Aptitude · Theoretical Distributions
For a normal distribution with mean 40 and standard deviation 5, approximately what percentage of observations lie between 30 and 50?
About 95.45% of observations lie between 30 and 50. These limits are the mean 40 plus and minus two standard deviations of 5 each, and the normal distribution has roughly 95.45% of its area within two standard deviations of the mean.
- A68.27%
- B95.45%Correct
- C99.73%
- D47.72%
Explanation
Z for 30 is (30 - 40)/5 = -2 and Z for 50 is +2. The area within mean ± 2 standard deviations is about 95.45%. The 68.27% figure is for ±1 sigma, and 47.72% covers only one side of the mean.
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