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The probability of an event occurring within 5 standard deviations from the mean is extremely rare, as it falls outside the normal range of outcomes.

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5mo ago

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Related Questions

In a standard normal distribution 95 percent of the data is within plus standard deviations of the mean?

95% is within 2 standard deviations of the mean.


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.


In a normal distribution what percentage of the data falls within 2 standard deviation of the mean?

In a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data is within 1 standard deviation, and about 99.7% is within 3 standard deviations. Therefore, the range within 2 standard deviations captures a significant majority of the data points.


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.


What percentage of scores falls between the mean and -2 to 2 standard deviations under the normal curve?

In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean (between -1 and +1 standard deviations). About 95% of scores fall within two standard deviations (between -2 and +2 standard deviations). Therefore, the percentage of scores that falls specifically between the mean and -2 to 2 standard deviations is about 95% minus the 50% that is below the mean, resulting in approximately 45%.


How does the bell curve relates to the empirical rule?

The bell curve, also known as the normal distribution, is a symmetrical probability distribution that follows the empirical rule. The empirical rule states that for approximately 68% of the data, it lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations when data follows a normal distribution. This relationship allows us to make predictions about data distribution based on these rules.


What is true in about a normal distribution?

A normal distribution is a symmetric, bell-shaped curve characterized by its mean and standard deviation. Approximately 68% of the data falls within one standard deviation from the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations, commonly referred to as the empirical rule. Additionally, the mean, median, and mode of a normal distribution are all equal and located at the center of the distribution. This property makes the normal distribution fundamental in statistics and probability theory.


What percentage of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution?

99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.


What percentage of a normal distribution is within 2 standard deviations of the mean?

I believe the standard deviations are measured from the median, not the mean.1 Standard Deviation is 34% each side of median, so that is 68% total.2 Standard Deviations is 48% each side of median, so that is 96% total.


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.


What percentage of data would fall within 1.75 standard deviations of the mean?

About 81.5%


In a normal standard curve approximately what percentages of scores will fall within 1 standard deviation from the mean?

In a normal standard curve, approximately 68% of scores fall within one standard deviation from the mean. This is part of the empirical rule, which states that about 95% of scores lie within two standard deviations, and about 99.7% fall within three standard deviations. Thus, the majority of data points are clustered around the mean.