There are two major tests of readiness for college, the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores are approximately normal with mean μ = 21.5 and standard deviation σ = 5.4. sat scores are reported on a scale from 600 to 2400. the sat scores are approximately normal with mean μ = 1498 and standard deviation σ = 316. alyssa scores 30 on the act. assuming that both tests measure the same thing, what score on the sat is equivalent to alyssa's act score? (round your answer to a whole number.)

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

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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