Total Ratings:
Total ratings for all employees:
\[ \text{Total} = 8 \times 30 = 240 \]
Top Five and Bottom Three Totals:
Total ratings for the top five employees:
\[ \text{Top Five Total} = 5 \times 38 = 190 \]
Total ratings for the bottom three employees:
\[ \text{Bottom Three Total} = 3 \times 25 = 75 \]
Verification of Totals:
Sum of ratings for all employees:
\[ \text{Sum of Top Five + Bottom Three} = 190 + 75 = 265 \]
This sum (265) exceeds the calculated total ratings of 240, indicating a discrepancy.
Analyze the Options:
(A) One of the top five employees has a rating of 50:
If one top employee's rating is 50, the remaining total for the other four is:
\[ 190 - 50 = 140, \quad \text{Average for four} = \frac{140}{4} = 35 \]
This scenario is plausible, as the remaining ratings are consistent with the data.
(B) The lowest rating among the bottom three employees is 20:
If one bottom employee's rating is 20, the remaining total for the other two is:
\[ 75 - 20 = 55, \quad \text{Average for two} = \frac{55}{2} = 27.5 \]
This scenario is plausible, as the calculated averages are consistent.
(C) The highest rating among the top five employees is 40:
If the highest rating among the top five is 40, the remaining total for the other four is:
\[ 190 - 40 = 150, \quad \text{Average for four} = \frac{150}{4} = 37.5 \]
This contradicts the given average of 38 for the top five, rendering this scenario impossible.
(D) One of the bottom three employees has a rating of 24:
If one bottom employee's rating is 24, the remaining total for the other two is:
\[ 75 - 24 = 51, \quad \text{Average for two} = \frac{51}{2} = 25.5 \]
This scenario is plausible, as it meets the stated conditions.
Thus, the correct answer is (C).