Question

8. ETS reports that GRE test takers had a mean Verbal score of M = 150.22...

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?

Homework Answers

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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