Standard Normal Distribution
Close
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Choose the correct answer below.
A. The mean and standard deviation have the values of $\mu=0$ and $\sigma=1$.
B. The mean and standard deviation have the values of $\mu=1$ and $\sigma=1$.
C. The mean and standard deviation have the values of $\mu=1$ and $\sigma=0$.
D. The mean and standard deviation have the values of $\mu=0$ and $\sigma=0$.

Step 1 ：A standard normal distribution is a special case of the normal distribution. It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one.

Step 2 ：The normal random variable of a standard normal distribution is called a standard score or a z-score.

Step 3 ：Every normal random variable X can be transformed into a z score via the following equation: z = (X - μ) / σ where μ is the mean of X and σ is the standard deviation of X.

Step 4 ：So, the correct answer should be A. The mean and standard deviation have the values of μ=0 and σ=1.

Step 5 ：Final Answer: \(\boxed{\text{A. The mean and standard deviation have the values of } \mu=0 \text{ and } \sigma=1}\).