Final answer:
The smallest possible value of the range is 8. The correct answer is D) 8.
Step-by-step explanation:
To find the smallest possible value of the range, we need to determine the range of values that satisfy the given conditions.
Since the mean is 12 and the median is 9, we know that the sum of the 7 values is 7 * 12 = 84 and the 4th value is 9. Using these two pieces of information, we can set up a system of equations:
x1 + x2 + x3 + 9 + x5 + x6 + x7 = 84
x4 = 9
Solving this system, we can find that x1 + x2 + x3 + x5 + x6 + x7 = 75. The smallest possible value for the range is when all the other values are equal to 1, giving us a range of 9 - 1 = 8.