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) .0005
B).002
C).025
D).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) .0005
B).002
C).025
D).045

Quizplus · Accepted Answer

To solve this problem, we will use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. First, we need to standardize the two scores we are interested in:

For a score of 400 or lower: Z = (400 - 500) / 100 = -1

For a score of 600 or higher: Z = (600 - 500) / 100 = 1

We can use a standard normal distribution table or a calculator to find the probabilities associated with these two Z-scores. For a Z-score of -1, the probability of getting a score of 400 or lower is about 0.16. For a Z-score of 1, the probability of getting a score of 600 or higher is also about 0.16.

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

P(400 or lower AND 600 or higher) = P(400 or lower) x P(600 or higher)

P(400 or lower AND 600 or higher) = 0.16 x 0.16

P(400 or lower AND 600 or higher) = 0.0256

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 test is 0.0256, which is closest to choice C (0.025).

Given That on One Section of the SAT the Mean