8. ETS reports that GRE test takers had a mean Verbal score of M = 150.22 and SD = 8.45. Assume the distribution of GRE Verbal scores is approximately normal in shape. Answer the following questions for the verbal portion of the GRE.
Source:
https://www.ets.org/s/gre/pdf/gre_interpreting_scores.pdf
(a) What percentage of students will score 139 or better on the verbal portion of the GRE?
(b) What percentage of students will score lower than 147?
Let X denote the Verbal score in GRE scored by a randomly selected test taker.
Given,
Mean, = 150.22
Standard deviation, = 8.45
(a) To find P(X ≥ 139)*100
Now, X can only take discrete values. So we approximate X to continuous to use Normal distribution
Thus, P(X ≥ 139) ≈ P(X > 138.5)
For X = 138.5, the corresponding Z value= (138.5 - 150.22)/8.45
= -1.387
Thus, P(X ≥ 138.5) = P(Z ≥ -1.387) =
So approximately 91.72% of the students will score 139 or better on the verbal portion of the GRE
(b) To find P(X < 147)*100
Approximating to continuous distribution,
P(X < 147) ≈ P(X < 146.5)
Corresponding Z value = (146.5 - 150.22)/8.45 = -0.44
Thus, P(X < 146.5) = P(Z < -0.44) = 0.33
So approximately 33% of students will score lower than 147
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