CA Foundation · Quantitative Aptitude · Theoretical Distributions
Which statement about the standard normal variate Z = (X - mu)/sigma is correct?
Z has mean 0 and standard deviation 1. Subtracting mu centres the distribution at zero and dividing by sigma rescales the spread to unity, so any normal variable converts to the standard normal variate and tables can be used.
- AZ has mean 1 and variance 0
- BZ has mean 0 and standard deviation 1Correct
- CZ has mean mu and standard deviation 1
- DZ has mean 0 and variance sigma squared
Explanation
Standardising subtracts the mean and divides by the standard deviation, so Z has mean 0 and SD 1. The other options misstate the mean or the spread.
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