CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is normally distributed with mean μ and variance σ², which transformation gives a variable that follows the standard normal distribution?
The standard normal variable is Z equal to X minus μ divided by σ. Subtracting the mean centres the distribution at zero, and dividing by the standard deviation, not the variance, scales it to have a standard deviation of one.
- A(X − μ)/σ²
- B(X − μ)/σCorrect
- C(X − σ)/μ
- D(X − μ)·σ
Explanation
The standard normal variable has mean 0 and SD 1. Subtracting μ makes the mean 0 and dividing by the standard deviation σ makes the SD 1. Dividing by σ² would give a variance of 1/σ², not 1, unless σ equals 1.
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