91影视

The table states the distribution of back-to-knee length for males and females.

The significantly high and low values are defined as $\text{P}\left(\text{x or greater}\right)猢�0.01$and $\text{P}\left(\text{x or less}\right)猢�0.01$ respectively.

Let X be the distribution of back-to-knee lengths of males.

Thus,

$$\begin{gathered} X~N\left(渭,{蟽}^2\right) \\ ~N\left(23.5,{1.1}^2\right) \end{gathered}$$

Let $x_1$ and $x_2$ be the minimum and maximum values such that, $\text{P}\left(X<x_1\right)=0.01$and $P\left(X>x_2\right)=0.01$.

Further,

$$\begin{gathered} P\left(X>x_2\right)=0.01 \\ 1-P\left(X<x_2\right)=0.01 \\ P\left(X<x_2\right)=0.99 \end{gathered}$$

The two values are shown on the graph below:

The cumulative area to the left of $x_1$ and $x_2$ is 0.01 and 0.99, respectively. Let the corresponding z-scores be $z_1$and $z_2$.

Thus,

$$\begin{gathered} P\left(Z<z_1\right)=0.01 \\ P\left(Z<z_2\right)=0.99 \end{gathered}$$

The z-score is obtained from the standard normal table:

• The intersection of row 2.3 and column 0.03 has the value 0.9901 (closest to 0.99). Thus, $z_2=2.33$.
• The intersection of row -2.3 and column 0.03 has the value 0.0099 (closest to 0.01). Thus, $z_1=-2.33$.

Relationship between x and corresponding z-score:

$z=\frac{x-渭}{蟽}$

Thus,

$$\begin{gathered} x_1=渭+z_1蟽 \\ =23.5+\left(-2.33\right)\left(1.1\right) \\ =20.9 \end{gathered}$$

$$\begin{gathered} x_2=渭+z_2蟽 \\ =23.5+\left(2.33\right)\left(1.1\right) \\ =26.1 \end{gathered}$$

Thus, it is concluded that the significantly high values are separated by 26.1 in., and significantly low are separated from not significant by 20.9 in.

Thus, the significantly high values are larger than 26.1 in. Therefore,

$P\left(26.1\text{or}\text{greater}\right)=0.01$

Thus, the significantly low values are larger than 20.9 in. Therefore,

$P\left(20.9\text{or}\text{less}\right)=0.01$

The measure of 26 in. lies to the left of 26.1 in., which implies it is not a significantly high value.