The required sentences can be completed as follows:
68% of the scores are between 68 and 84.
95% of the scores are between 60 and 92.
99.7% of the scores are between 52 and 100.
To complete the first sentence, we need to find the range of scores that includes 68% of the values.
We know that 68% of the scores fall within 8 points of the mean, so the range of scores that includes 68% of the values is 76 - 8 to 76 + 8, or 68 to 84.
Therefore, the first sentence can be completed as follows:
68% of the scores are between 68 and 84.
To complete the second sentence, we need to find the range of scores that includes 95% of the values.
We know that 95% of the scores fall within 16 points of the mean, so the range of scores that includes 95% of the values is 76 - 16 to 76 + 16, or 60 to 92.
Therefore, the second sentence can be completed as follows:
95% of the scores are between 60 and 92.
To complete the third sentence, we need to find the range of scores that includes 99.7% of the values.
We know that 99.7% of the scores fall within 24 points of the mean, so the range of scores that includes 99.7% of the values is 76 - 24 to 76 + 24, or 52 to 100.
Therefore, the third sentence can be completed as follows:
99.7% of the scores are between 52 and 100.
Learn more about the empirical rules here:
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