Using the health records of ever student at a high school, the school nurse created a scatterplot relating y= text{height (in centimeters) to} x= text

Given: (Equation population regression line): ${\displaystyle {\mu }_y=105+4.2x}$
${\displaystyle \sigma =7}$ The average height of 15-year-old students at this high scool according to the population regression line can be found by replacing x in the regression line equation by 15 and evaluating. ${\displaystyle {\mu }_y=105+4.2\left(15\right)=105+63=168}$ Thus the mean is 168 and the standard deviation is7. Since the conditions are met, the response y varies according to a Normal distribution. The z-score is the value decreased by the mean, divided by the standard deviation. ${\displaystyle z=\frac{x-\mu }{\sigma }=\frac{180-168}{7}\approx 1.71}$ Determine the corresponding probability using the normal probability table in the appendix. ${\displaystyle P\left(Z<1.71\right)}$ is given in the row starding with 1.7 and in the column starting with .01 of the standard normal probability table in the appendix. ${\displaystyle P\left(X>180\right)=P\left(Z>1.71\right)}$
${\displaystyle =1-P\left(Z<1.71\right)}$
${\displaystyle =1-0.9564}$
${\displaystyle =0.0436}$
${\displaystyle =4.36\mathrm{\%}}$ Thus about ${\displaystyle 4.36\mathrm{\%}}$ of the 15-year-old students at this scool are expected to be taller than 180 cm.