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When a data set is normally distributed about how much of the data fall within one standard deviation of the mean?
In a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean. This is part of the empirical rule, which states that about 68% of the data lies within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations.
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When a data set is normally distributed about how much of the data fall within two standard deviations of the mean?
In a normally distributed data set, approximately 95% of the data falls within two standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data falls within one standard deviation and about 99.7% falls within three standard deviations. Therefore, two standard deviations capture a significant majority of the data points.
Why is it that only one normal distribution table is needed to find any probability under the normal curve?
Anything that is normally distributed has certain properties. One is that the bulk of scores will be near the mean and the farther from the mean you are, the less common the score. Specifically, about 68% of anything that is normally distributed falls within one standard deviation of the mean. That means that 68% of IQ scores fall between 85 and 115 (the mean being 100 and standard deviation being 15) AND 68% of adult male heights fall between 65 and 75 inches (the mean being 70 and I am estimating a standard deviation of 5). Basically, even though the means and standard deviations change, something that is normally distributed will keep these probabilities (relative to the mean and standard deviation). By standardizing these numbers (changing the mean to 0 and the standard deviation to 1) we can use one table to find the probabilities for anything that is normally distributed.
Assume that aset of test scores is normally distributed with a mean of 100 and a standard deviation of 20 use the 68-95-99?
68% of the scores are within 1 standard deviation of the mean -80, 120 95% of the scores are within 2 standard deviations of the mean -60, 140 99.7% of the scores are within 3 standard deviations of the mean -40, 180
What percentage of the data falls within 3 standard deviation of the mean?
Approximately 99.7% of the data falls within 3 standard deviations of the mean in a normal distribution. This is known as the empirical rule or the 68-95-99.7 rule, which describes how data is distributed in a bell-shaped curve. Specifically, about 68% of the data falls within 1 standard deviation, and about 95% falls within 2 standard deviations of the mean.
If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches then approximately 68 of all women should be between and inches in height.?
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Given a mean height of 65 inches and a standard deviation of 2.5 inches, this means that approximately 68% of women will have heights between 62.5 inches (65 - 2.5) and 67.5 inches (65 + 2.5).
What percentage of the normally distributed population lies within the plus or minus one standard deviation of the population mean?
68.2%
When a data set is normally distributed about how much of the data fall within two standard deviations of the mean?
In a normally distributed data set, approximately 95% of the data falls within two standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data falls within one standard deviation and about 99.7% falls within three standard deviations. Therefore, two standard deviations capture a significant majority of the data points.
Why is it that only one normal distribution table is needed to find any probability under the normal curve?
Anything that is normally distributed has certain properties. One is that the bulk of scores will be near the mean and the farther from the mean you are, the less common the score. Specifically, about 68% of anything that is normally distributed falls within one standard deviation of the mean. That means that 68% of IQ scores fall between 85 and 115 (the mean being 100 and standard deviation being 15) AND 68% of adult male heights fall between 65 and 75 inches (the mean being 70 and I am estimating a standard deviation of 5). Basically, even though the means and standard deviations change, something that is normally distributed will keep these probabilities (relative to the mean and standard deviation). By standardizing these numbers (changing the mean to 0 and the standard deviation to 1) we can use one table to find the probabilities for anything that is normally distributed.
Assume that aset of test scores is normally distributed with a mean of 100 and a standard deviation of 20 use the 68-95-99?
68% of the scores are within 1 standard deviation of the mean -80, 120 95% of the scores are within 2 standard deviations of the mean -60, 140 99.7% of the scores are within 3 standard deviations of the mean -40, 180
The percentage that is one standard deviation away from mean?
For normally distributed data. One standard deviation (1σ)Percentage within this confidence interval68.2689492% (68.3% )Percentage outside this confidence interval31.7310508% (31.7% )Ratio outside this confidence interval1 / 3.1514871 (1 / 3.15)
What percentage of the data falls within 3 standard deviation of the mean?
Approximately 99.7% of the data falls within 3 standard deviations of the mean in a normal distribution. This is known as the empirical rule or the 68-95-99.7 rule, which describes how data is distributed in a bell-shaped curve. Specifically, about 68% of the data falls within 1 standard deviation, and about 95% falls within 2 standard deviations of the mean.
What is the approximate percentage score of less than 140 using the 68-95-99.7 rule if a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20?
The 68-95-99.7 rule states that in a normally distributed set of data, approximately 68% of all observations lie within one standard deviation either side of the mean, 95% lie within two standard deviations and 99.7% lie within three standard deviations.Or looking at it cumulatively:0.15% of the data lie below the mean minus three standard deviations2.5% of the data lie below the mean minus two standard deviations16% of the data lie below the mean minus one standard deviation50 % of the data lie below the mean84 % of the data lie below the mean plus one standard deviation97.5% of the data lie below the mean plus two standard deviations99.85% of the data lie below the mean plus three standard deviationsA normally distributed set of data with mean 100 and standard deviation of 20 means that a score of 140 lies two standard deviations above the mean. Hence approximately 97.5% of all observations are less than 140.
If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches then approximately 68 of all women should be between and inches in height.?
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Given a mean height of 65 inches and a standard deviation of 2.5 inches, this means that approximately 68% of women will have heights between 62.5 inches (65 - 2.5) and 67.5 inches (65 + 2.5).
Is empirical rule a characteristic of a normal distribution?
Yes, the empirical rule, also known as the 68-95-99.7 rule, is a characteristic of a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and around 99.7% lies within three standard deviations. This rule helps in understanding the spread and variability of data in a normally distributed dataset.
How are scores distributed if the mean is 100 and the standard deviation is 15?
If the mean score is 100 and the standard deviation is 15, the distribution of scores is likely to follow a normal distribution, also known as a bell curve. In this distribution, approximately 68% of scores fall within one standard deviation of the mean (between 85 and 115), about 95% fall within two standard deviations (between 70 and 130), and about 99.7% fall within three standard deviations (between 55 and 145). This pattern indicates that most scores cluster around the mean, with fewer scores appearing as you move away from the center.
How many of scores will be within 1 standard deviation of the population mean?
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
What Percent of population between 1 standard deviation below the mean and 2 standard deviations above mean?
In a normal distribution, approximately 68% of the population falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Therefore, to find the percentage of the population between one standard deviation below the mean and two standard deviations above the mean, you would calculate 95% (within two standard deviations) minus 34% (the portion below one standard deviation), resulting in approximately 61% of the population.
