Evaluate the integral. ∫50∫25−x2√−25−x2√∫25−x2−z2√−25−x2−z2√1(x2+y2+z2)1/2dydzdx∫05∫−25−x225−x2∫−25−x2−z225−x2−z21(x2+y2+z2)1/2d
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Answer:
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.
