Let us evaluate the sum [tex]\(\sum(z + 2.5)\)[/tex] where [tex]\(z\)[/tex] takes the values given in the table: 12, 14, 0, 8, 9, and 11.
Step-by-Step Solution:
1. List the values of [tex]\(z\)[/tex]:
[tex]\[
z = [12, 14, 0, 8, 9, 11]
\][/tex]
2. Add 2.5 to each value of [tex]\(z\)[/tex]:
[tex]\[
z_1 = 12 + 2.5 = 14.5
\][/tex]
[tex]\[
z_2 = 14 + 2.5 = 16.5
\][/tex]
[tex]\[
z_3 = 0 + 2.5 = 2.5
\][/tex]
[tex]\[
z_4 = 8 + 2.5 = 10.5
\][/tex]
[tex]\[
z_5 = 9 + 2.5 = 11.5
\][/tex]
[tex]\[
z_6 = 11 + 2.5 = 13.5
\][/tex]
3. Sum all the modified values:
[tex]\[
\sum (z + 2.5) = 14.5 + 16.5 + 2.5 + 10.5 + 11.5 + 13.5
\][/tex]
[tex]\[
\sum (z + 2.5) = 69.0
\][/tex]
Therefore, the evaluated sum [tex]\(\sum(z + 2.5) = 69.0\)[/tex].
