Question

Rob had a test average of 85.6 last semester. His first four test grades were 78, 92, 94, and 80. Use the formula x‾=x1+x2+…+xnn to find his score on the fifth test.

Answer 1

Given the equation:

`\bar{x}=(x_1+x_2+x_3+x_4+x_5)/(n)`

In this question:

x- = 85.6

x₁ = 78

x₂ = 92

x₃ = 94

x₄ = 80

x₅ = missing

n = 5

Substitute the values and then solve for x₅.

`\begin{gathered} 85.6=(78+92+94+80+x_5)/(5) \\ 85.6=(344+x_5)/(5) \\ \text{ Multiplying both sides by 5:} \\ 85.6*5=(344+x_5)/(5)*5 \\ 428=344+x_5 \\ \text{ Subtracting 344 from both sides:} \\ 428-344=344-344+x_5 \\ 84=x_5 \end{gathered}`

Answer: 84.