Given:
Mean score, μ = 73
Standard deviation, σ = 6
z-score = 2
Let's find the number of points you scored.
Apply the z-score formula:
[tex]Z=\frac{x-u}{\sigma}[/tex]WHere:
x is the actual score
z is the z-score = 2
σ is the standard deviation = 6
μ is the average = 73
Let's rewrite the formula for x, which is the actual score.
Multiply both sides by σ :
[tex]\begin{gathered} Z\sigma=\frac{x-\mu}{\sigma}\ast\sigma \\ \\ Z\sigma=x-\mu \\ \\ \text{Add }\mu\text{ to both sides:} \\ Z\sigma+\mu=x-\mu+\mu \\ \\ Z\sigma+\mu=x \\ \\ x=Z\sigma+\mu \end{gathered}[/tex][tex]x=Z\sigma+\mu[/tex]Hence, we have:
[tex]\begin{gathered} x=2(6)+73 \\ \\ x=12+73 \\ \\ x=85 \end{gathered}[/tex]The number of points scored is 85
ANSWER:
85
