The ACT Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 27 and a standard deviation of 3. Assuming these raw scores form a normal distribution. What scoreseparates the lower 35% of the distribution?

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ANSWER:

the score is 25.86

SOLUTION:

The formula for Z-score is

[tex]Z\text{ = }\frac{x-\operatorname{mean}}{\text{st. dev}}[/tex]

From the Z-score table, since it is 0.35 or 35%, we will look into the negative Z values. And the Z-score value close to 0.35 is -0.38. You can get the -table value here (https://www.ztable.net/)

Substituting this to the equation, we can get the value of x

[tex]\begin{gathered} -0.38\text{ = }\frac{x-27}{3} \\ x\text{ =2}5.86 \end{gathered}[/tex]