Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution. The proportion of students scoring at least 600 is closest to:
A)0.082.
B)0.184.
C)0.218.
D)0.782.

Question

Quizplus · Accepted Answer

We first need to standardize the score of 600 using the formula:

Z = (X - μ) / σ

Where X is the score we want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Substituting the values we get:

Z = (600 - 515) / 109 = 0.780

Now we need to find the proportion of scores above this value. Using a standard normal distribution table or calculator, we find:

P(Z > 0.780) = 0.218

Therefore, the proportion of students scoring at least 600 is approximately 0.218 or 21.8%. The closest answer choice is (C).

Scores on the SAT Verbal Test in Recent Years Follow