1 out of 10 attempts The average fulltime faculty member in

1 out of 10 attempts The average full-time faculty member in a post-secondary degree granting institution works an average of 51 hours per week. Round intermediate calculations and final answers to two decimal places as needed. 1% of faculty members work a. If we assume the standard deviation is 2.7 hours, more than 56.4 hours a week. 1% of faculty members work more than b. If we assume a bell-shaped distribution, 56.4 hours a week.

Solution

1. The average full-time faculty....

a)

56.4 is k = 2 standard deviations above the mean, 51.

Hence, by Chebyshev\'s theorem, those above this valie is

1/(2k^2) = 1/(2*2^2) = 0.125 or 12.5% [ANSWER]

*************************

b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    56.4      
u = mean =    51      
          
s = standard deviation =    2.7      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 = 2.28% [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!