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Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance.

For a particular EMS station ambulance response time is known to be normally distributed with m = 7.5 minutes and s = 2.5 minutes.

猞�

Let X be the random variable which represents the ambulance response time with mean $渭$and variance ${蟽}^2$. That is $\mathrm{渭}=7.5\min {\mathrm{蟽}}^2=2.5\min$

Calculating Z-value of$X_1$

$$\begin{gathered} Z_1=\frac{X_1-渭}{蟽} \\ =\frac{9-7.5}{2.5} \\ =\frac{1.5}{2.5} \\ =0.6 \end{gathered}$$

If area A is 90% or more than 90%, then regulations are met at EMS station A.

猞�

Let t=2 minutes.

If probability of getting $X_2=2$ is less than 0.05, then it is unlikely that call was service by station A. That is

If area $A_2<0.05$

Therefore t is unlikely that call was serviced by station A.

Hence,

$$\begin{gathered} Z_1=\frac{X_2-渭}{蟽} \\ =\frac{2-7.5}{2.5} \\ {Z}_2=-2.2 \end{gathered}$$

From Z-table $Z_2=-2.2$, therefore $A_2=0.014$

Since $A_2\left(0.014\right)<0.05$, it is unlikely that the call was serviced by Station A.