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Question 320293: Which of the following is TRUE about the standard deviation of a normal distribution?
A. The standard deviation is the line of symmetry of the normal curve.
B. The graph of the normal curve is higher or taller when the standard deviation is larger.
C. The standard deviation does not influence the graph of a normal distribution.
D. The standard deviation describes how much of the data are spread out and affects the line of symmetry.
The
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Answer is B as far as I can see.
The standard deviation tells you what percentage of the scores are a certain value.
That would be represented by the area under the curve.
If your x-axis are the scores and your y-axis are the percentage of the scores that are a certain value, then the following is true:
A smaller standard deviation will have more of the scores closer to the mean which means the curve will be higher and narrower.
A larger standard deviation will have more of the scores further away from the mean which means the curve will be lower and wider.
That fits selection B the best.
The standard deviation does not affect the line of symmetry in a normal distribution.
That is always in the middle regardless of how fat or skinny the curve is.
The line of symmetry is the mean of the distribution when the distribution is normal.
A distribution of scores with a smaller standard deviation might be represented by a curve where 90% of the scores are at the mean. Since the area under the curve cannot be greater than 100%, this means that there's only 10% of the curve to represent the remaining scores. That makes a very tall and narrow curve.
A distribution of scores with a larger standard deviation might be represented by a curve where 50% of the scores are at the mean. Since the area under the curve cannot be greater than 100%, this means that there's 50% of the curve to represent the remaining scores. That makes a shorter and wider curve.
The mean will always be in the middle of the normal distribution so the symmetry of the curve is not changed, only the shape. 50% of the scores will still be below the mean and 50% of the scores will still be above the mean.
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