Respuesta :
Applying statistical concepts, it is found that the values are:
- p = -11.37
- q = 81
When a constant is added to each data in a variable:
- The mean is incremented by this constant.
- The variance remains constant.
When a constant is multiplied to each data in a variable:
- The mean is multiplied by this constant.
- The variance is multiplied by the square of this constant
Hence, mean of 12, added with p and multiplied with q, for a mean of 51:
[tex](12 + p)q = 51[/tex]
Variance of 84, after the operations, 756:
[tex]84\sqrt{q} =756[/tex]
[tex]\sqrt{q} = \frac{756}{84}[/tex]
[tex]\sqrt{q} = 9[/tex]
[tex](\sqrt{q})^2 = 9^2[/tex]
[tex]q = 81[/tex]
For p:
[tex](12 + p)q = 51[/tex]
[tex](12 + p)81 = 51[/tex]
[tex]12 + p = \frac{51}{81}[/tex]
[tex]12 + p = 0.63[/tex]
[tex]p = -11.37[/tex]
A similar problem is given at https://brainly.com/question/24097242
