CA Foundation · Quantitative Aptitude · Theoretical Distributions
The marks in an aptitude test are normally distributed. 15.87% of candidates score below 40 and 2.28% score above 70. Using P(Z < -1) = 0.1587 and P(Z > 2) = 0.0228, what are the mean and standard deviation of the marks?</br>
The mean is 50 and the standard deviation is 10. The tail areas give Z = -1 at 40 and Z = +2 at 70, so 40 = mu - sigma and 70 = mu + 2sigma. Solving gives sigma = 10 and mu = 50.
- AMean 50, SD 10Correct
- BMean 55, SD 5
- CMean 45, SD 15
- DMean 50, SD 15
Explanation
Below 40 at 15.87% gives (40 - mu)/sigma = -1. Above 70 at 2.28% gives (70 - mu)/sigma = 2. Subtracting: 30 = 3 sigma, so sigma = 10, and mu = 40 + 10 = 50. Check: (70-50)/10 = 2. Option 50 with SD 15 fails since (40-50)/15 is not -1.
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