Question

work hours for college faculty the average full - time faculty member in a post - secondary degree granting institution works an average of 57 hours per week. round intermediate calculations and final answers to two decimal places as needed. part: 0 / 2 part 1 of 2 (a) if we assume the standard deviation is 2.1 hours, then no more than 5.56% of faculty members work more than 63.3 hours a week.

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 63.3$, $\mu=57$, and $\sigma = 2.1$.
$z=\frac{63.3 - 57}{2.1}=\frac{6.3}{2.1}=3$

Step2: Use the empirical rule

For a normal distribution, about 99.7% of the data lies within $z=\pm3$. So the proportion of data outside $z = 3$ (in the right - tail) is $\frac{1 - 0.997}{2}$.
$\frac{1 - 0.997}{2}=\frac{0.003}{2}=0.0015 = 0.15\%$

Answer:

$0.15\%$