a sample of assistant professors on the business faculty at the largest college in ontario revealed the mean…

a sample of assistant professors on the business faculty at the largest college in ontario revealed the mean annual income to be $62,000 with a standard deviation of $3,000. using the empirical rule, what proportion of faculty earn more than $56,000 but less than $68,000?\n a. approximately 95%\n b. almost all\n c. approximately 68%\n d. at least 50%\n e. at least 75%

a sample of assistant professors on the business faculty at the largest college in ontario revealed the mean annual income to be $62,000 with a standard deviation of $3,000. using the empirical rule, what proportion of faculty earn more than $56,000 but less than $68,000?\n a. approximately 95%\n b. almost all\n c. approximately 68%\n d. at least 50%\n e. at least 75%

Answer

Explanation:

Step1: Calculate z-score for 56000

$z_1 = \frac{56000 - 62000}{3000} = -2$

Step2: Calculate z-score for 68000

$z_2 = \frac{68000 - 62000}{3000} = 2$

Step3: Apply Empirical Rule

For $z=\pm2$, the proportion within this range is ~95%.

Answer:

a. Approximately 95%