Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 400 seconds and a standard deviation of 50 seconds.

suppose there are 144 emergencies in that town.

in about how many emergencies are the response times expected between 350 seconds and 450 seconds?
49
51
96
98

Step-by-step explanation:

In the normal distribution curve, the mean is in the middle and each line to the left and to the right of that mean represent 1- and 1+ the standard deviation.  If our mean is 400, then 400 + 50 = 450; 450 + 50 = 500; 500 + 50 = 550.  Going from the mean to the left, we subtract the standard deviation and 400 - 50 = 350; 350 - 50 = 300; 300 - 50 = 250.  We are interested in the range that falls between 350 and 450 as a percentage.  That range represents the two middle sections, each containing 34% of the data.  So the total percentage of response times is 68%.  We are looking then for 68% of the 144 emergency response times in town.  .68(144) = 97.92 or 98 emergencies that have response times of between 350 and 450 seconds.

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