Question

Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 450 seconds and a standard deviation of 50 seconds.

Suppose there are 97 emergencies in that town.

In about how many emergencies are the response times expected between 400 seconds and 500 seconds?

Answer 1

for mean \(\mu = 450\) and SD \(\sigma = 50\), you are looking at response times falling within \(400 \to 500 \) or \(\mu - \sigma \to \mu + \sigma \).

\(P( \mu - \sigma \le X \le \mu + \sigma ) = 0.6827 \). you can use z-scores if you like but that is well known number.

so ~68% of all emergencies have a response time within those limits

and so you can estimate that ~68% of your 97 emergencies will also fall within those limits

Answer 2

@sillybilly123 thanks so much for your help :)

Answer 3

mp!