Answer:
A refund must be above $7,139 before it is audited.
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 = 7010, standard deviation = 43.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
The empirical rule is symmetric, which means that the lowest (100-99.7)/2 = 0.15% is at least 3 standard deviations below the mean, and the upper 0.15% is at least 3 standard deviations above the mean.
Use the Empirical Rule to determine approximately above what dollar value must a refund be before it is audited.
3 standard deviations above the mean, so:
7010 + 3*43 = 7139.
A refund must be above $7,139 before it is audited.
