Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are at least $74,000?
A) It is about 68%.
B) It is about 84%.
C) It is about 95%.
D) It is about 97.5%.

Question

Quizplus · Accepted Answer

Given the distribution is approximately bell-shaped (normal distribution), we can use the empirical rule. A salary of $74,000 is one standard deviation below the mean ($80,000 - $74,000 = $6,000). According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, which means about 34% is below and 34% is above one standard deviation from the mean. Since we are looking for salaries at least $74,000, we add the 34% above one standard deviation to the 50% that falls within the first standard deviation to the mean, totaling approximately 84%.

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