Question 1175386: The American Automobile Association reports that the
average time it takes to respond to an emergency call is
28 minutes. Assume the variable is approximately
normally distributed and the standard deviation is 9.002
minutes. If 70 calls are randomly selected, approximately
how many will be responded to in less than 15 minutes? How many will be responded to in 50 percent ? hwo many will be 100 percent?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sigma/sqrt(n)
< (15-28)/9.002/sqrt(70)
<-13*sqrt(70)/9.002
<-12.078
probability is essentially 0 meaning 0 calls will be responded to in < 15 minutes.
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The wording isn't clear after that. How many will be responded to in 50% of what? If it is 50% of the calls are responded to, using the word approximately, 14 of the 28.
100%, mathematically, infinite time. Realistically, greater than 3 std errors, a SE being sd/sqrt(n) or 9.002/sqrt(70)=1.076, so 3 SE are 3.228 min or waiting time of 31.32 minutes.
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