Question

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.

Answer 1

The proportion of students scoring at least 600 is closest to:

C) 0.218

Step-by-step explanation:

The given question provides information about the distribution of scores on the SAT verbal test, stating that they follow approximately the normal distribution N(515, 109). To find the proportion of students scoring at least 600, we need to standardize the score and then find the corresponding area under the normal curve.

First, we calculate the z-score using the formula:
`\( z = ((X - \mu))/(\sigma) \), where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \)`is the standard deviation. For
`\( X = 600 \), \( \mu = 515 \), and \( \sigma = 109 \), the z-score is \( z = ((600 - 515))/(109) \approx 0.7798 \).`

Next, we look up the corresponding area to the right of this z-score in the standard normal distribution table. The area is approximately 0.218. Therefore, the proportion of students scoring at least 600 is closest to 0.218.

In conclusion, the final answer is C) 0.218, as it represents the calculated proportion of students scoring at least 600 based on the given normal distribution parameters.