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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 160 emergencies in that town.

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

51

55

80

109

Mar 25, 2019

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$$\text{Let }\Phi(x) \text{ be the CDF of the standard normal, (that thing you have the table for)}\\ P[\text{response between 400 and 500 seconds}] = \\ \Phi\left(\dfrac{500-450}{50}\right) - \Phi\left(\dfrac{400-450}{50}\right)=\\ \Phi(1)-\Phi(-1) \approx 0.683\\ 0.683 \times 160 \approx 109.23$$

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Mar 25, 2019

$$\text{Let }\Phi(x) \text{ be the CDF of the standard normal, (that thing you have the table for)}\\ P[\text{response between 400 and 500 seconds}] = \\ \Phi\left(\dfrac{500-450}{50}\right) - \Phi\left(\dfrac{400-450}{50}\right)=\\ \Phi(1)-\Phi(-1) \approx 0.683\\ 0.683 \times 160 \approx 109.23$$