Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes: Mean call-to-shock time, x 2 6 7 9 12 Survival rate, y 90 45 31 4 3 The data were used to compute the equation of the least-squares line, which was ŷ = 101.16 − 9.24x.A newspaper article reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain. Since the slope of the least-squares line is −9.24, we can say that every extra minute waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 9.24 percentage points. Since the slope of the least-squares line is −101.16, we can say that every extra minute waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10.116 percentage points. There is not enough information from the least-squares line to make such a statement. Since the slope of the least-squares line is 101.16, we can say that every extra minute waiting for paramedics to arrive with a defibrillator raises the chance of survival by 10.116 percentage points. Since the slope of the least-squares line is 9.24, we can say that every extra minute waiting for paramedics to arrive with a defibrillator raises the chance of survival by 9.24 percentage points.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered?
The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes:
Mean call-to-shock time, x
2
6
7
9
12
Survival rate, y
90
45
31
4
3
The data were used to compute the equation of the least-squares line, which was
ŷ = 101.16 − 9.24x.
A newspaper article reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain.
Since the slope of the least-squares line is −9.24, we can say that every extra minute waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 9.24 percentage points.
Since the slope of the least-squares line is −101.16, we can say that every extra minute waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10.116 percentage points.
There is not enough information from the least-squares line to make such a statement.
Since the slope of the least-squares line is 101.16, we can say that every extra minute waiting for paramedics to arrive with a defibrillator raises the chance of survival by 10.116 percentage points.
Since the slope of the least-squares line is 9.24, we can say that every extra minute waiting for paramedics to arrive with a defibrillator raises the chance of survival by 9.24 percentage points.
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