Answer:
To find the probability that a student scored above 500 on the GMAT, we need to calculate the z-score and then use the standard normal distribution table.
The z-score can be calculated using the formula:
z = (x - μ) / σ
Where:
x = the value we are interested in (500 in this case)
μ = the mean (average) GMAT score (631)
σ = the standard deviation (80)
Now, let's calculate the z-score:
z = (500 - 631) / 80
z = -131 / 80
z ≈ -1.6375
Next, we look up the corresponding area/probability in the standard normal distribution table for a z-score of -1.6375. This table gives us the probability of getting a value less than the given z-score.
From the table, we find that the area/probability corresponding to a z-score of -1.6375 is approximately 0.0502.
Since we want the probability of scoring above 500, we subtract this probability from 1:
P(score > 500) = 1 - 0.0502
P(score > 500) ≈ 0.9498
Therefore, the probability that a student scored above 500 on the GMAT is approximately 0.9498, rounded to the nearest ten-thousandth.