About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?

Short Answer

Expert verified

Approximately 95%of x values lies within two standard deviation.

Step by step solution

01

Given Information 

The empirical rule additionally alluded to as the three-sigma rule or 68-95-99.7 rule, is a factual decision that expresses that for a normal distribution, practically totally noticed information will fall inside three standard deviations of the mean or normal

02

Explanation 

The Empirical Rule expresses that 99.7%of information noticed observing an normal distribution exists in 3standard deviations of the mean. Under this standard, 68%of the information falls inside one standard deviation, 95%percent inside two standard deviations, and 99.7%inside three standard deviations from the mean.

Therefore, about 95%percent of xvalues from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution.

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Suppose X~N(15,3). Between what xvalues does 68.27%of the data lie? The range of xvalues is centered at the mean of the distribution (i.e., 15).

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