91Ó°ÊÓ

A $15$to $18$-year-old male from Chile was $176cm$tall from $2009$to $2010$.

It is given that,

$X~N(170,6.28)$

Where,

$\mathrm{μ}=170$

$\mathrm{σ}=6.28$

And,

$x=176$

So, the $z$-score at $x=176$will be:

$z-score=\frac{176-\mathrm{μ}}{\mathrm{σ}}$

$=\frac{176-170}{6.28}$

$≈0.9554$

It is known that by using the $z$-score it can be measured that by how many standard deviations $\left(\mathrm{σ}\right)$, the value of $x$ will lie below (left) or above (right) the mean $\left(\mathrm{μ}\right)$ of the distribution. The $z$-score will be negative if the value of mean is greater than the value of $x$ or $x$ lies below (left) of the mean and it will be positive if the value of mean is less that than the value of $x$ or above (right) of the mean.

So, it is clear that this score tells that $x=176$ is $0.9554$ standard deviations to the right of the mean $170$.

The height of a $15$ to $18$-year-old male from Chile from $2009$to $2010$.

$(z=-2)$The value of $x$or male's height can be calculated as below:

$z-\text{score}=\frac{x-\mathrm{μ}}{\mathrm{σ}}$

$-2=\frac{x-170}{6.28}$

$x-170=-2×6.28$

$x=157.44$

Therefore, the value of $x$or male's height is $157.44$centimeters.

This $z$-score $(z=-2)$tells that the male's height is $2$standard deviation to the left of the mean.