Given that on one section of the SAT the mean is 500 and the standard deviation is 100,what is the approximate probability of a student scoring 300 or lower or 700 or higher on the test?
A) .124
B).022
C).045
D).245

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 a student scoring 300 or lower or 700 or higher on the test? 
A) .124
B).022
C).045
D).245

Quizplus · Accepted Answer

To solve this, we need to find the z-scores for both 300 and 700.

Z-score for 300: 
z = (300-500)/100 = -2

Z-score for 700: 
z = (700-500)/100 = 2

Now, we need to find the area to the left of -2 and the area to the right of 2 on a standard normal distribution table (or using a calculator).

The area to the left of -2 is approximately 0.0228, and the area to the right of 2 is also approximately 0.0228.

Therefore, the approximate probability of scoring 300 or lower or 700 or higher is the sum of these two probabilities:

P(Z ≤ -2) + P(Z ≥ 2) = 0.0228 + 0.0228 = 0.0456

Rounded to the nearest thousandth, the answer is 0.045, which corresponds to choice C.

Given That on One Section of the SAT the Mean