If the random variable X is normally distributed with mean and standard deviation ,then the random variable Z defined by is also normally distributed with mean 0 and standard deviation 1.

Question

If the random variable X is normally distributed with mean  and standard deviation  ,then the random variable Z defined by  is also normally distributed with mean 0 and standard deviation 1.

Quizplus · Accepted Answer

This statement is true. Any standard normal variable (Z) can be obtained by subtracting the mean of the original normal variable (X) and dividing it by its standard deviation. So, if X is normally distributed with mean μ and standard deviation σ, then the standardized variable Z = (X-μ)/σ is also normally distributed with mean 0 and standard deviation 1.

If the Random Variable X Is Normally Distributed with Mean