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For the Standard Normal distribution, what percentage of data is within 1.50 standard deviations of the mean? What percentage of data is more than 1.50 standard deviations from the mean?

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Final answer:

Approximately 34% of the data is within 1.50 standard deviations of the mean in the Standard Normal distribution. Approximately 12% of the data is more than 1.50 standard deviations from the mean.

Step-by-step explanation:

The Standard Normal Distribution, also known as the Z-distribution, is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. In this distribution, approximately 68% of the data falls within one standard deviation of the mean, which means that 34% of the data is within 0.5 standard deviations on either side of the mean.

Since 1.50 standard deviations is equivalent to 1.50 times the standard deviation of 1 in the Z-distribution, we can find the percentage of data within this range. Using the Empirical Rule, we know that approximately 88% of the data is within two standard deviations of the mean. Therefore, we can subtract this percentage (88%) from 100% to find the percentage of data that is more than 1.50 standard deviations from the mean, which is 12%.

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