91影视

The data for sitting back-to-knee length for adult males and females are provided.

The left tailed area is equal to the cumulative probabilities, which are obtained by using the standard normal table (Table A-2) for z-scores.

In the case of finding the right-tailed areas, the difference of these cumulative probabilities from 1 gives the required area towards the right of the z-score.

Let Y represent the back-to-knee length of females.

$$\begin{gathered} Y~N\left(渭,{蟽}^2\right) \\ ~N\left(22.7,{1.0}^2\right) \end{gathered}$$

Let y be the value of length separating the bottom 25% of lengths from the top 75%, with a corresponding z-score z.

The shaded area in the graph shows the 25% bottom region corresponding to value y.

Then,

$$\begin{gathered} P\left(Y<y\right)=0.25 \\ P\left(Z<z\right)=0.25 \end{gathered}$$

Where

$z=\frac{y-渭}{蟽}$

Use the standard normal table;the area of 0.25 is observed corresponding to the row value -0.6 and the column value 0.07. This implies that the z score is -0.67.

The length is computed as:

$$\begin{gathered} \frac{y-渭}{蟽}=-0.67 \\ \frac{y-22.7}{1.0}=-0.67 \\ x=\left(-0.67脳1.0\right)+22.7 \\ =22.0 \end{gathered}$$

Therefore, the length separating the bottom 25% from the top 75% is $Q_1=22in$.