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The distribution of heights for $15$-year-old males is symmetric, single-peaked, and bell-shaped.

z-score of $0$corresponds to a heightlocalid="1649751998639" $=170cm$

z-score of $1$corresponds to a height of localid="1649752004677" $=177.5cm$

Find the z-score corresponding to Paul鈥檚 height.

Given:

$$\begin{gathered} x=179\mathrm{cm} \\ 渭=170\mathrm{cm} \\ 蟽=7.5\mathrm{cm} \end{gathered}$$

In other words, it is the mean divided by the standard deviation divided by the value of the $z-$score

$z=\frac{x-渭}{蟽}=\frac{179-170}{7.5}=1.20$

localid="1649752085470" $1.2$standard deviations above the mean, Paul's height is higher than the average.

The distribution of heights for$15$-year-old males is symmetric, single-peaked, and bell-shaped.

z-score of$0$corresponds to a height of

localid="1649752116086" $z-$score of $1$corresponds to a height oflocalid="1649752017672" $=177.5cm$

Given:

Paul's height$=85th$percentile

As a percentage, the $xth$percentile represents a value that has$x\%$of the other values below it.

A $15-$year-old male who is taller than Paul exceeds $85\%$of the entire population.