Question

The average GMAT scores for students entering the graduate school of business at UGA was 631. Assuming scores are normally distributed and the standard deviation is 80, what is the probability that a student scored above 500? Write your probability as a decimal rounded to the nearest ten-thousandth.

Answer 1

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.