Question

Lynette, a student in the class, is $65$ inches tall. Find and interpret her z-score.

Short answer

$z-$score is the$-0.466$.

Step-by-step solution

Step 1. Given

A dot plot shows the height distribution in the class, as well as summary data from the computer output.

Step 2. Concept

Value that has been standardized (z-score) The standardized value of $x$is $z=\frac{x-mean}{s\tan darddeviation}$if $x$is an observation from a distribution with known mean and standard deviation. A $z-$score is a term used to describe a standardized value.

Step 3. Explanation

If $x$is an observation from a distribution that has known mean and standard deviation, standardized score for$x$is,

$z=\frac{x-mean}{s\tan darddeviation}$

So here, $x=65$

And from the given dot plot $x=67$and standard deviation is $S_x=4.09$

$z=\frac{65-67}{4.29}$

$z=-0.466$