CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is a normal variate with mean 40 and standard deviation 8, which of the following describes the standard normal variate Z obtained from X?
Z = (X − 40)/8 is correct. Standardisation subtracts the mean (40) and divides by the standard deviation (8), not the variance. The resulting variable Z has mean 0 and variance 1, which defines the standard normal distribution used with Z-tables.
- AZ = (X − 8)/40, with mean 0 and variance 1
- BZ = (X − 40)/8, with mean 0 and variance 1Correct
- CZ = (X − 40)/8, with mean 1 and variance 0
- DZ = (X − 40)/64, with mean 0 and variance 1
Explanation
The standard normal variate is formed by subtracting the mean and dividing by the standard deviation: Z = (X − 40)/8. It always has mean 0 and variance 1. Dividing by 64 uses the variance instead of the standard deviation, which is wrong.
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