Question

mr. navards statistics class decided measure and record their heights in inches. the summary statistics are below: mean height $\bar{x}$ standard deviation of heights $s_x$ 67 inches 4.29 one of the students lynette is 65 inches tall. which of the following is her z - score and the correct interpretation of it? o $z = 0.446$; lynettes height is 0.446 inches above the mean height of the class. o $z=-0.446$; lynettes height is 0.446 inches below the mean height of the class. o $z = 0.466$; lynettes height is 0.466 standard deviations above the mean height of the class. o $z=-0.466$; lynettes height is 0.466 standard deviations below the mean height of the class.

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\bar{x}}{s_x}$, where $x$ is the individual value, $\bar{x}$ is the mean, and $s_x$ is the standard deviation.

Step2: Identify the values

We are given that $\bar{x} = 67$ inches, $s_x=4.29$, and $x = 65$ inches.

Step3: Calculate the z - score

Substitute the values into the formula: $z=\frac{65 - 67}{4.29}=\frac{- 2}{4.29}\approx - 0.466$.
The negative sign indicates that the value is below the mean. A z - score of $-0.466$ means that Lynette's height is 0.466 standard deviations below the mean height of the class.

Answer:

$z=-0.466$; Lynette's height is 0.466 standard deviations below the mean height of the class.