Question

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?

Answer #1

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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