91影视

The time $蠂$ is exponentially distributed with the mean:

$\begin{array}{c}渭=10\\ 蟽\text{=0.10}\\ \text{E}\left(\text{蠂}\right)=渭=0.10\end{array}$

$\begin{array}{c}\text{V}\left(\text{蠂}\right)={蟽}^2={\left(0.1\right)}^2\\ =0.01\end{array}$

The calculation is given below:

Now, $蠂$represents the sample mean period for n = 50

localid="1651469168306" $\stackrel{-}{蠂}=\frac{{\text{蠂}}_{\text{1}}+{\text{蠂}}_2+\mathrm{.......}+{\text{蠂}}_{50}}{50}$

$\begin{array}{c}\text{E}\left(\stackrel{-}{蠂}\right)=\frac{1}{50}\text{E}({\text{蠂}}_{\text{1}}+{\text{蠂}}_2+\mathrm{.......}+{\text{蠂}}_{50})\\ =\frac{1}{50}(\text{E}\left({\text{蠂}}_{\text{1}}\right)+\text{E}\left({\text{蠂}}_2\right)+\mathrm{.......}+\text{E}\left({\text{蠂}}_{50}\right))\\ =\frac{1}{50}(渭+渭+50\text{times+}渭)\\ =\frac{50渭}{50}\end{array}$

localid="1651469270820" $=0渭$

$\text{E}\left(\stackrel{-}{蠂}\right)=0.1$

localid="1651469378610" $\begin{array}{c}\text{V}\left(\stackrel{-}{蠂}\right)=\text{V}\left(\frac{{\displaystyle \underset{i鈮�1}{\overset{50}{鈭�}}脳\text{i}}}{50}\right)\\ =\frac{1}{{\left(50\right)}^2}\text{V}(\underset{i鈮�1}{\overset{50}{鈭�}}脳\text{i})\\ =\frac{1}{2500}\underset{i鈮�1}{\overset{50}{鈭�}}脳\text{V}\left(\text{蠂颈}\right)\\ =\frac{1}{2500}\underset{i鈮�1}{\overset{50}{鈭�}}{蟽}^2\end{array}$

localid="1651469435234" $\begin{array}{c}=\frac{1}{2500}脳500{蟽}^2\\ =\frac{{蟽}^2}{50}\\ =\frac{0.01}{50}\end{array}$

$\text{V}\left(\stackrel{-}{蠂}\right)=0.0002$

The $\text{E}\left(\stackrel{-}{蠂}\right)=0.1$or$渭\left(\stackrel{-}{蠂}\right)andV\left(\stackrel{-}{蠂}\right)=0.0002=蟽{\text{蠂}}^{\text{2}}$. Then using the control limit theorem $\stackrel{-}{蠂}~\text{N}\left(渭{\text{蠂}}_{\text{1}}蟽{\text{蠂}}_2\right)$that is$\stackrel{-}{蠂}~\text{N}(0.001,0.002).$It is since n =50 that is the higher size of the sample $(>30)$.

The calculation is given below:

$\begin{array}{c}\text{P}\left(\text{Samplemeantime>0.13}\right)=\text{P}\left(\text{.13}\right)\\ =\text{P}(\frac{鈭�0.01}{\sqrt{0.002}}>\frac{0.13鈭�0.01}{\sqrt{0.002}})=\text{P}(z>8.49)\\ =0\end{array}$