Question

what requirements are necessary for a normal probability distribution to be a standard normal probability distribution? the mean and standard deviation have the values of μ = 1 and σ = 1. the mean and standard deviation have the values of μ = 0 and σ = 1. the mean and standard deviation have the values of μ = 0 and σ = 0. the mean and standard deviation have the values of μ = 1 and σ = 0.

Explanation:

A standard normal distribution is a special case of the normal distribution. By definition, it has a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1. Let's check each option:

• Option 1: $\mu = 1$ and $\sigma=1$ is just a normal distribution, not the standard normal distribution.
• Option 2: $\mu = 0$ and $\sigma = 1$ satisfies the definition of a standard normal distribution.
• Option 3: $\sigma=0$ would mean all data points are at the mean (since there is no spread), which is not a normal (or standard normal) distribution.
• Option 4: $\mu = 1$ and $\sigma = 0$ is also not a standard normal distribution (due to $\sigma=0$ and wrong $\mu$ value).

Answer:

The mean and standard deviation have the values of $\mu = 0$ and $\sigma=1$ (the second option).