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 percent.
B)68 percent.
C)75 percent.
D)95 percent.

Question

Quizplus · Accepted Answer

According to Chebyshev's inequality, at least 75% of the data will fall within two standard deviations of the mean.

In this case, the range from $68,000 to $92,000 is within two standard deviations from the mean ($80,000), so we can use Chebyshev's inequality to determine the minimum percentage of salaries falling within this range:

- At least 1 - (1/2^2) = 75% of the data falls within two standard deviations of the mean.

Therefore, the minimum percentage of salaries falling between $68,000 and $92,000 is 75%.

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