Question

Another student in the class, Brent, is $74$ inches tall. How tall is Brent compared with the rest of the class? Give appropriate numerical evidence to support your answer.

Short answer

Brent's height is $1.63$ standard deviations above the mean.

Step-by-step solution

Step 1. Given

Dot plot of the class’s height distribution along with summary statistics from 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 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, so standardized score for $x$is, $z=x-mean/s\tan darddeviation$

As a result, it is stated that,

$x=74$

And, based on the dot plot provided, $x=67$and the standard deviation of the data $S_x=4.29$

$z=$ $\frac{74-67}{4.29}$

$z=1.63$