91影视

The Mean and Standard deviation,

For Wendy:

For Jill:

For Carmen:

For Latrice:

When Both X and Y are independent,

Property mean:

${渭}_{aX+bY}=a{渭}_X+b{渭}_Y$

Property variance:

${蟽}_{aX+bY}^2=a^2{渭}_X^2+b^2{渭}_Y^2$

Now,

The sum of each swimmer's mean times is the mean of overall time:

$\begin{array}{rcl}{渭}_{X_1+X_2+X_3+X_4}& =& {渭}_{X_1}+{渭}_{X_2}+{渭}_{X_3}+{渭}_{X_4}\\ & =& 55.2+58.0+56.3+54.7\\ & =& 224.2\text{seconds}\end{array}$

We are aware of this.

The square root of variance is standard deviation:

$蟽X_1+X_2+X_3+X_4=\sqrt{{蟽}_{X_1}^2+{蟽}_{X_2}^2+{蟽}_{X_3}^2+{蟽}_{X_4}^2}=\sqrt{(2.8{)}^2+(3.0{)}^2+(2.6{)}^2+(2.7{)}^2}$

$鈮�5.5579$seconds

To Calculate the z - score:

$z=\frac{x-渭}{蟽}=\frac{220-224.2}{5.5579}鈮�-0.76$

To find the relevant probability, use Table - A:

$\begin{array}{rcl}P(X& <& 220)=P(z<-0.76)\\ & =& 0.2236\end{array}$

Thus,

The likelihood that the total team time in the 400-meter freestyle relay is fewer than 220 seconds in a randomly selected race is $0.2236$.