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A normal distribution has a mean of 4 and a standard deviation of 1. What percent of values are from 2 to 6?

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Final answer:

Approximately 95% of the values lie within two standard deviations of the mean in a normal distribution.

Since the range from 2 to 6 constitutes two standard deviations from the mean of 4 in this scenario, about 95% of the values would fall in this range.

Step-by-step explanation:

To find what percent of values from a normal distribution with a mean (μ) of 4 and a standard deviation (σ) of 1 are between 2 and 6, we use the Empirical Rule, which is very helpful for normal distributions.

The rule states that approximately 68% of data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the range from 2 to 6 is two standard deviations from the mean (2 = 4 - 2σ and 6 = 4 + 2σ).

Thus, according to the Empirical Rule, approximately 95% of the values lie within two standard deviations of the mean, which is the range we are interested in.

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