Answer:
The percentage of people taking the test who score between 489 and 573 is 34%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 573, standard deviation of 84
Percentage of people taking the test who score between 489 and 573
The mean is 573.
489 = 573 - 84, which means that 489 is one standard deviation below the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are below the mean.
So between one standard deviation below the mean and the mean, the percentage is 68/2 = 34%
The percentage of people taking the test who score between 489 and 573 is 34%.
