Question

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.

Answer 1

d. It is at most 25 percent.

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.