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Answer:
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.
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.
- 68% of the scores are between  Within 1 standard deviation 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.
- 95% of the scores are between , Within 2 standard deviations of the mean.
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.
- 99.7% of the scores are between , Within 3 standard deviations of the mean. Â
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.
For the more information about Standard deviation click the link given below.
https://brainly.com/question/16307869
