CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is normally distributed with mean 40 and variance 25, which of the following gives the distribution of Y = 2X + 10?
Y is normal with mean 90 and variance 100. The mean becomes 2 times 40 plus 10, which is 90, and the variance is multiplied by 2 squared, giving 100, while the added constant does not affect variance.
- ANormal with mean 90 and variance 100Correct
- BNormal with mean 90 and variance 50
- CNormal with mean 80 and variance 100
- DNormal with mean 90 and variance 110
Explanation
Mean of Y = 2(40) + 10 = 90. Variance of Y = 2² × 25 = 100; the constant 10 does not change variance. Variance 50 wrongly multiplies by 2 instead of 4, and mean 80 omits the added 10.
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