Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000.Using Chebyshev's inequality,the percentage of salaries falling between $68,000 and $92,000 is at least __________.
A) 65%
B) 68%
C) 75%
D) 95%

Question

Quizplus · Accepted Answer

Chebyshev's inequality states that at least (1 - 1/k^2) of the data falls within k standard deviations of the mean. Here, $68,000 and $92,000 are $12,000 away from the mean, which is 2 standard deviations ($12,000/$6,000 = 2). So, at least (1 - 1/2^2) = 75% of the salaries fall within this range.

Professors at a Local University Earn an Average Salary of $80,000