Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution cannot be regarded as bell-shaped. What can be said about the percentage of salaries that are less than $68,000 or more than or more than $92,000? choices belowa. It is at least 75 percent. b. It is at least 55 percent. c. It is at least 25 percent. d. It is at most 25 percent.

d. It is at most 25 percent.

Step-by-step explanation:

When the distribution is not normal, we use the Chebyshev's theorem, which states that:

At least 75% of the measures are within 2 standard deviations of the mean

At least 89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 80,000

Standard deviation = 6,000

What can be said about the percentage of salaries that are less than $68,000 or more than or more than $92,000?

68000 = 80000 - 2*6000

So 68000 is two standard deviations below the mean

92000 = 80000 + 2*6000

So 92000 is two standard deviations above the mean.

By Chebyshev's Theorem, at least 75% of the salaries are between $68,000 and $92,000. Others, which are at most 25%, are either less than $68,000 or more than $92,000.

So the correct answer is:

d. It is at most 25 percent.