Respuesta :
standardized z score for the act result = (30 - 21.5) / 5.4 = 1.574
so for the sat ressult we have 1.574 = (X - 1498) / 316
X = 316 * 1.574 + 1498 = 1995 answer
so for the sat ressult we have 1.574 = (X - 1498) / 316
X = 316 * 1.574 + 1498 = 1995 answer
Assuming that both tests measure the same thing, the equivalent sat score is 1994
The given parameters are:
ACT scores
Mean, μ = 21.5
Standard deviation, σ = 5.4
Score, x = 30
SAT scores
Mean, μ = 1498
Standard deviation, σ = 316
Start by calculating the z-score for the act score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{30 - 21.5}{5.4}[/tex]
[tex]z = 1.57[/tex]
Next, calculate the z-score for the sat score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{x - 1498}{316}[/tex]
Substitute 1.57 for z
[tex]1.57 =\frac{x - 1498}{316}[/tex]
Multiply both sides by 316
[tex]496.12 =x - 1498[/tex]
Solve for x
[tex]x = 496.12 + 1498[/tex]
[tex]x = 1994.12[/tex]
Approximate
[tex]x = 1994[/tex]
Hence, the equivalent sat score is 1994
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