CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is normally distributed with mean 80 and standard deviation 12, and Y = 2X + 10, what are the mean and standard deviation of Y?
Y has mean 170 and standard deviation 24. Doubling X doubles its mean to 160 and its standard deviation to 24, and adding 10 shifts only the mean to 170, leaving the spread unchanged because a constant does not affect dispersion.
- AMean 170, SD 24Correct
- BMean 170, SD 34
- CMean 160, SD 24
- DMean 90, SD 12
Explanation
A linear transformation of a normal variable is normal. Mean of Y = 2(80) + 10 = 170. SD of Y = 2 × 12 = 24, since the constant 10 shifts the mean but does not affect spread. Adding 10 to the SD gives the wrong 34.
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