the final grade averages from a fictional graduate statistics class are uniformly distributed between 66 and 96. what is the probability that a student selected at random will have a final average of between 90 and 100?

To find the probability that a student selected at random will have a final average between 90 and 100, we need to calculate the proportion of the total range that falls within this range.

Given that the final grade averages are uniformly distributed between 66 and 96, we can determine the total range by subtracting the lower bound from the upper bound:

Total Range = Upper Bound - Lower Bound = 96 - 66 = 30

Next, we find the range between 90 and 100:

Target Range = Upper Range - Lower Range = 100 - 90 = 10

To calculate the probability, we divide the target range by the total range:

Probability = Target Range / Total Range = 10 / 30 = 1/3

Therefore, the probability that a student selected at random will have a final average between 90 and 100 is 1/3.