Final answer:
80% of samples will have less than 44.944% of minority students.
Step-by-step explanation:
To find the answer to this question, we can use the normal distribution and the standard deviation formula.
First, we need to find the standard deviation, which is the square root of the product of the probability of success and the probability of failure, divided by the sample size.
In this case, the probability of success is 45% and the probability of failure is 55%. So, the standard deviation is sqrt((0.45 * 0.55) / 75) = 0.069.
Then, we can use a Z-table to find the cumulative probability up to a given Z-score.
In this case, we want to find the Z-score that corresponds to 80% of samples having less than a certain percentage of minority students.
We can use the formula Z = (x - mean) / standard deviation, where x is the desired percentage and mean is the average percentage of minority students.
The mean is 45% and the standard deviation is 0.069. So, we can plug these values in and solve for x: 0.8 = (x - 45) / 0.069.
Solving for x, we find x = 45 - (0.069 * 0.8) = 44.944.
So, 80% of samples will have less than 44.944% of minority students.