Question

Define the value of the mean, standard deviation, and variance in a standard normal distribution. the standard deviation of any standard normal distribution is .

a.) 0.5
b.) 1
c.) 2
d.) 0

Answer 1

The standard normal distribution is uniquely defined by a mean of 0 and standard deviation of 1. The variance, being the square of the standard deviation, is also 1 in a standard normal distribution. Therefore, the correct answer to the question is (b) 1.

Step-by-step explanation:

The standard normal distribution is a specific kind of normal distribution that is used extensively in statistics. By definition, this distribution has a mean (μ) of 0 and a standard deviation (σ) of 1. This means that all values in a standard normal distribution can be described in terms of standard deviations from the mean.

For example, a value with a z-score of 1 is one standard deviation above the mean, and a value with a z-score of -2 is two standard deviations below the mean.

The variance, another measure of spread, is the square of the standard deviation, which in the case of a standard normal distribution would be 1² or just 1.

It's important to note that in the context of the standard normal distribution, the standard deviation is always 1, which means the correct answer to the question is option (b) 1.