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The scores on a test administered to prospective employees are normally distributed with a mean of 100 and a standard deviation of 15.

About what percent of the scores are between 70 and 130?

Answer :

Final answer:

In the context of a normal distribution, about 95% of values are within 2 standard deviations from the mean. As the given scores of 70 and 130 are each 2 standard deviations away from the mean of 100, approximately 95% of the test scores fall between these two values.

Explanation:

This question can be addressed using the properties of normal distribution and standard deviations. When a set of data is normally distributed, approximately 68% of it is within 1 standard deviation from the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Here, the mean score is 100 and the standard deviation is 15. A score of 70 is 2 standard deviations below the mean (100 - 2*15) and a score of 130 is 2 standard deviations above the mean (100 + 2*15).

Therefore, the scores between 70 and 130 include 2 standard deviations on either side of the mean. Based on the properties of normal distribution, we know that 2 standard deviations encompass approximately 95% of the data. Therefore, we conclude that approximately 95% of the scores are between 70 and 130.

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