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19 January, 03:57

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 288 emergencies in that town. in about how many emergencies are the response times expected between 400 seconds and 500 seconds?

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  1. 19 January, 04:48
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    The number of emergencies between 400 sec and 500 sec will be determined as follows:

    z = (x-μ) / σ

    but

    n=288

    thus

    when x=400

    z = (400-450) / 50=-1

    P (z<-1) = 0.4602

    When x=500

    z = (500-450) / 50=1

    P (z<1) = 0.5398

    Hence:

    P (400
    =0.5398-0.4602

    =0.0796

    thus the number of cases will be:

    0.0796*288

    =22.9~23 emergency cases
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