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.
