Hi Steve,

A quick and naive approach:
Enter into cells A1:D4:
=INT(RAND()*(C2-C1+1))+C1 Min -6
=INT(RAND()*(C2-C1+1))+C1 Max 14
=INT(RAND()*(C2-C1+1))+C1 Average =AVERAGE(A1:A40) 4.2
=INT(RAND()*(C2-C1+1))+C1 Accuracy 0.05
Copy A4 down to A40.
Now you can push F9 until the average comes near to your desired result or
you insert a macro like:
Option Explicit

Public Sub try()
Dim i As Long

i = 1
With Sheets("Sheet1")
Do While i < 100
.Calculate
If Abs(.Cells(3, 3) - .Cells(3, 4)) <= .Cells(4, 3) Then
Exit Do
End If
i = i + 1
Loop
End With
End Sub

HTH,
Bernd