Answer:
number 4: frequency 8
number 5; frequency 2
Explanation:
The mean of all rolls is their sum divided by their number, which is 30. Let x and y represent the number of rolls of 4 and 5, respectively. Then the mean is ...
(1×6 +2×3 +3×5 +4x +5y +6×6)/30 = 3.5
This simplifies to ...
(6 +6 +15 +4x +5y +36) = 3.5×30 . . . . . multiply by 30
4x +5y = 42 . . . . . . subtract 63
Of course, the total number of rolls must be 30:
6 +3 +5 +x +y +6 = 30
x + y = 10
We can solve this system of equations by substitution, using x=10-y:
4(10 -y) +5y = 42
40 +y = 42
y = 2
x = 10 -2 = 8
The two missing numbers are 8 and 2. The frequency of 4 is 8; the frequency of 5 is 2.