91影视

${渭}_A=50$

${蟽}_A=10$

${渭}_E=25$

${蟽}_E=5$

Properties mean and variance:

${渭}_{aX+bY}=a{渭}_X+b{渭}_Y$

${蟽}_{aX+bY}^2=a^2{蟽}_X^2+b^2{蟽}_Y^2$

We can then determine the mean and variance of $D=A-E$:

localid="1650079367506" $$\begin{gathered} {渭}_D={渭}_{A-E} \\ ={渭}_A-{渭}_E \\ =50-25 \\ =25 \end{gathered}$$

localid="1650079383160" $$\begin{gathered} {蟽}_D^2={蟽}_{A-E}^2 \\ ={蟽}_A^2+{蟽}_E^2 \\ ={10}^2+5^2 \\ =125 \end{gathered}$$

The standard deviation is the square root of the variance:

localid="1650079394752" $$\begin{gathered} {蟽}_D=\sqrt{{蟽}_D^2} \\ =\sqrt{125} \\ 鈮�11.1803 \end{gathered}$$

${渭}_A=50$

${蟽}_A=10$

${渭}_E=25$

${蟽}_E=5$

Properties mean and variance:

${渭}_{aX+bY}=a{渭}_X+b{渭}_Y$

${蟽}_{aX+bY}^2=a^2{蟽}_X^2+b^2{蟽}_Y^2$

We can then determine the mean and variance of $D=A-E$:

localid="1650079432625" $$\begin{gathered} {渭}_D={渭}_{A-E} \\ ={渭}_A-{渭}_E \\ =50-25 \\ =25 \end{gathered}$$

The standard deviation is the square root of the variance:

localid="1650079466152" $$\begin{gathered} {蟽}_D=\sqrt{{蟽}_D^2} \\ =\sqrt{125} \\ 鈮�11.1803 \end{gathered}$$

The z-score is the value decreased by the mean, divided by the standard deviation:

$z=\frac{x-渭}{蟽}=\frac{0-25}{11.1803}鈮�-2.24$

$z=\frac{x-渭}{蟽}=\frac{0-25}{11.1803}鈮�-2.24$

Determine the corresponding probability using table A:

localid="1650079488846" $$\begin{gathered} P(E>A)=P(D<0) \\ =P(Z<-2.24) \\ =0.0125 \\ =1.25\% \end{gathered}$$