Given that on one section of the SAT the mean is 500 and the standard deviation is 100, what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test?
A)0.0005
B)0.002
C)0.025
D)0.045

Question

Given that on one section of the SAT the mean is 500 and the standard deviation is 100, what is the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the test?​
A)0.0005
B)0.002
C)0.025
D)0.045

Quizplus · Accepted Answer

To solve this problem, we can use the z-score formula:

z = (x - mean) / standard deviation

For the first event (selecting a student with a score of 400 or lower), we have:

z = (400 - 500) / 100 = -1

Using a z-table, we can find that the probability of selecting a student with a z-score of -1 or lower is approximately 0.1587.

For the second event (selecting a student with a score of 600 or higher), we have:

z = (600 - 500) / 100 = 1

Using the same z-table, we can find that the probability of selecting a student with a z-score of 1 or higher is approximately 0.1587.

To find the probability of both events happening, we can multiply their probabilities together:

0.1587 * 0.1587 = 0.025

Therefore, the approximate probability of selecting a student whose score is 400 or lower followed by selecting a student whose score is 600 or higher on the SAT is 0.025 or 2.5%, which corresponds to choice C.

Given That on One Section of the SAT the Mean