Business Degree Certification Practice Test

According to Chebyshev's Theorem, what proportion of the faculty earns more than $26,000 but less than $38,000 if the mean income is $32,000 with a standard deviation of $3,000?

1. At least 50%

2. At least 25%

3. At least 75%

4. At least 100%

The correct answer is: At least 75%

Chebyshev's Theorem provides a way to quantify the proportion of values that lie within a specified number of standard deviations from the mean in any distribution, regardless of its shape. In this scenario, the mean income is $32,000 with a standard deviation of $3,000. The income range you are considering is between $26,000 and $38,000. To analyze this, determine how many standard deviations away from the mean these values are. 1. For the lower limit of $26,000: - The distance from the mean is $32,000 - $26,000 = $6,000. - This distance corresponds to $6,000 / $3,000 = 2 standard deviations below the mean. 2. For the upper limit of $38,000: - The distance from the mean is $38,000 - $32,000 = $6,000. - This distance corresponds to $6,000 / $3,000 = 2 standard deviations above the mean. Thus, the range from $26,000 to $38,000 spans 2 standard deviations below and above the mean income of $32,000. According to Chebyshev's The