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Question

**Ambulance response time**. Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when thepatient is reached by ambulance. Geographical Analysis (Vol. 41, 2009) investigated the characteristics of ambulance response time for EMS calls in Edmonton, Alberta. For a particular EMS station (call it Station A), ambulance response time is known to be normally distributed with $\mu=7.5$ minutes and $\sigma=2.5$ minutes. A randomly selected EMS call in Edmonton has an ambulance response time of 2 minutes. Is it likely that this call was serviced by Station A? Explain.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 5Given:
$$\begin{aligned}
\mu&=\text{Mean}=5.26
\\ \sigma&=\text{Standard deviation}=10
\end{aligned}$$
We need to determine the probability $P(x<2)$. When the probability is large (greater than 0.05), then it is likely that the call was serviced by Station A.
To derive the probability, we first convert the $x$-value to a z-score and then use the "normal curve areas" table to derive the probability.

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