Question

standard normal distribution z - score the normal distribution with a mean of and a standard deviation of. the number of (a) that the data value is above or below the (μ). every data value in a data set has a corresponding z - score. x = data value μ = mean σ = standard deviation z = (x - μ)/σ

Explanation:

Step1: Recall z - score concept

The z - score measures the number of standard deviations a data value is from the mean. A positive z - score indicates the data value is above the mean ($\mu$), and a negative z - score indicates the data value is below the mean.

Step2: Fill in the blanks

The number of standard deviations a data value is above or below the mean is given by the z - score. The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation. In a normal distribution with a mean of $\mu$ and a standard deviation of $\sigma$, every data value in a data set has a corresponding z - score.

Answer:

(a) standard deviations; (b) mean; (c) $\sigma$; (d) $\frac{x-\mu}{\sigma}$