Final answer:
The percentage of students who received a merit scholarship but did not receive enough to cover full tuition is 10.2%, which when rounded to the nearest whole percent is 10%. Since 10% is not one of the provided options, there may be an error in the provided options or the question itself.
Step-by-step explanation:
To calculate the percentage of students who received a merit scholarship but did not receive enough to cover full tuition, we need to look at the distribution of the scholarship amounts and compare it to the cost of full tuition at Big State University. The scholarships are distributed normally with a mean of $3,450 and a standard deviation of $470. The full tuition cost is $4,050.
We first calculate the z-score for the tuition cost using the formula for a z-score:
z = (X - μ) / σ, where X is the value (full tuition), μ is the mean, and σ is the standard deviation. Therefore,
z = ($4,050 - $3,450) / $470 ≈ 1.277.
Using the z-table or standard normal distribution table, we find the area to the left of z = 1.277. This area represents the percentage of students who received enough to cover the full tuition. However, we want the area to the right, which represents those who did not receive enough.
To find this area, we subtract the area to the left from 1. If the area to the left is approximately 0.898, then the area to the right is 1 - 0.898 = 0.102 or 10.2%. Given the options provided, none of them are a direct match, so we use rounding rules to determine the closest percent.
When rounding to the nearest whole percent, 10.2% is rounded to 10%, which is not an option in the list provided. If the options are a typographical error and 10% was intended, then that would be the answer. However, if the options provided are correct, then this answer indicates there may be a mistake in the question or the answer choices.