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 92 46 31 6 3 (a) Construct a scatterplot for these data. A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13.The vertical axis is labeled "y" and has values from 0 to 100.1 point is plotted at approximately (2, 2.5).4 points are plotted in an almost straight line from approximately (6, 5) up and right to approximately (12, 92.5).A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13.The vertical axis is labeled "y" and has values from 0 to 100.1 point is plotted at approximately (12, 2.5).4 points are plotted in an almost straight line from approximately (2, 92.5) down and right to approximately (9, 5).A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100.The vertical axis is labeled "y" and has values from 0 to 13.1 point is plotted at approximately (2.5, 2).4 points are plotted in an almost straight line from approximately (5, 6) up and right to approximately (92.5, 12).A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100.The vertical axis is labeled "y" and has values from 0 to 13.1 point is plotted at approximately (2.5, 12).4 points are plotted in an almost straight line from approximately (5, 9) down and right to approximately (92.5, 2). How would you describe the relationship between mean call-to-shock time and survival rate? There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve. (b) Find the equation of the least-squares line. (Round your values to three decimal places.) ŷ = + x(c) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)
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, x
2
6
7
9
12
Survival rate, y
92
46
31
6
3
(a)
Construct a
A scatterplot has 5 points.
The horizontal axis is labeled "x" and has values from 0 to 13.
The vertical axis is labeled "y" and has values from 0 to 100.
1 point is plotted at approximately (2, 2.5).
4 points are plotted in an almost straight line from approximately (6, 5) up and right to approximately (12, 92.5).
A scatterplot has 5 points.
The horizontal axis is labeled "x" and has values from 0 to 13.
The vertical axis is labeled "y" and has values from 0 to 100.
1 point is plotted at approximately (12, 2.5).
4 points are plotted in an almost straight line from approximately (2, 92.5) down and right to approximately (9, 5).
A scatterplot has 5 points.
The horizontal axis is labeled "x" and has values from 0 to 100.
The vertical axis is labeled "y" and has values from 0 to 13.
1 point is plotted at approximately (2.5, 2).
4 points are plotted in an almost straight line from approximately (5, 6) up and right to approximately (92.5, 12).
A scatterplot has 5 points.
The horizontal axis is labeled "x" and has values from 0 to 100.
The vertical axis is labeled "y" and has values from 0 to 13.
1 point is plotted at approximately (2.5, 12).
4 points are plotted in an almost straight line from approximately (5, 9) down and right to approximately (92.5, 2).
How would you describe the relationship between mean call-to-shock time and survival rate?
There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve.
There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.
There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve.
There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.
(b)
Find the equation of the least-squares line. (Round your values to three decimal places.)
ŷ = +
x
(c)
Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)
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