Problem 108E

Ambulance response time. 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. 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 µ= 7.5 minutes and σ= 2.5 minutes.

a. Regulations require that 90% of all emergency calls should be reached in 9 minutes or less. Are the regulations met at EMS Station A? Explain.

b. 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 :

Step 1 of 2:

Given for a particular EMS station ambulance response time is known to be normally distributed with mean = 7.5 per minute and standard deviation =2.5 minute.

Our goal is :

a). We need to find are the regulation met at EMS station and explain.

b). We need to find is it likely that this call was serviced by station A and explain.

a).

Given regulations require that 90% of all emergency call be reached in 9 minute or less.

Now we have to find are the regulation met at EMS station.

The formula for the z score is

z =

We know that and .

Here x = 9.

Then,

z =

z =

z = 0.6

Therefore, z=0.6.

Then the probability of x is less than or equal to 9 is

P(x9) = P(z0.6)

From area under the normal table.

P(x9) = 0.7257

Hence this probability is less than 0.90, then the regulations are not being met at EMS station A.

b).

Given a randomly selected EMS call in Edmonton has an ambulance response time of 2 minute.

Now we have to find is it likely that this call was serviced by station A.

The formula for the z score is

z =

We know that and .

Here x = 2.

Then,

z =

z =

z = -2.2

Therefore, z=-2.2.

Then the probability of x is less than or equal to 2 is

P(x2) = P(z-2.2)

From area under the normal table.

P(x2) = 0.0179

Hence this probability is so small, so it would be very unlikely that the call was service by Station A.