Question

a companys annual income tax data for 2021 shows a mean annual employee income of $55,000, with a standard deviation of annual income of $12,000. 2021 taxable income taxable income distribution what percentage of employees have an annual income between $31,000 and $79,000? 68% 50% 95% 99.7%

Explanation:

Step1: Recall the empirical rule for normal - distribution

In a normal distribution, about 99.7% of the data lies within 3 standard - deviations of the mean.

Step2: Calculate the range within 3 standard - deviations

Let the mean $\mu = 55000$ and the standard deviation $\sigma=12000$.
The lower limit of the range within 3 standard - deviations is $\mu - 3\sigma=55000-3\times12000=55000 - 36000 = 19000$.
The upper limit of the range within 3 standard - deviations is $\mu + 3\sigma=55000 + 3\times12000=55000+36000 = 91000$.
The range from 31000 to 79000 is also within 3 standard - deviations of the mean.
Since about 99.7% of the data in a normal distribution lies within 3 standard - deviations of the mean, the percentage of employees with an annual income between 31000 and 79000 is 99.7%.

Answer:

99.7%