G A set of exam scores is normally distributed with a mean = 76 and standard deviation = 9. Use the Empirical Rule to complete the following sentences. 68% of the scores are between Incorrect and Incorrect. 95% of the scores are between Incorrect and Incorrect. 99.7% of the scores are between Incorrect and Incorrect

68% of the scores are between 67 and 85.

95% of the scores are between 58 and 94.

99.7% of the scores are between 49 and 103.

Given that,

Set of exam scores is normally distributed with a mean = 76

And standard deviation = 9.

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

We have to determine,

Empirical rule to complete the following statements.

According to the question,

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Then, mean - standard deviation = 76 - 9 = 67

And mean + standard deviation= 76 + 9 = 85

68% of the scores are between 67 and 85.

Then, mean - 2× standard deviation = 76 - 2×9 = 58

mean +2 × standard deviation = 76 + 2×9 = 94

95% of the scores are between 58 and 94.

Then, mean - 3 × standard deviation = 76 - 3× 9 = 49

mean + 3 × standard deviation = 76 + 3×9 = 103

99.7% of the scores are between 49 and 103.

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68% of the scores are between 67 and 85.

95% of the scores are between 58 and 94.

99.7% of the scores are between 49 and 103.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 76

Standard deviation = 9

68% of the scores are between

Within 1 standard deviation of the mean. So

76 - 9 = 67

76 + 9 = 85

68% of the scores are between 67 and 85.

95% of the scores are between

Within 2 standard deviations of the mean. So

76 - 2*9 = 58

76 + 2*9 = 94

95% of the scores are between 58 and 94.

99.7% of the scores are between

Within 3 standard deviations of the mean. So

76 - 3*9 = 49

76 + 3*9 = 103

99.7% of the scores are between 49 and 103.