Final answer:
The percentage of WFU students who pay less than $700 for rent is approximately 26.21%. The rent value that corresponds to the 45th percentile is approximately $728.08.
Step-by-step explanation:
To answer part (a) of the student's question, we want to find the percentage of students who pay less than $700 for rent when the amount spent is normally distributed with a mean of $735 and a standard deviation of $55. We will use the Z-score formula, which is Z = (X - μ) / σ, where X is the value ($700), μ is the mean ($735), and σ is the standard deviation ($55). After calculating the Z-score, we will refer to the standard normal distribution table to find the percentage of students.
For part (b), to find the rent value that corresponds to the 45th percentile, we need to look up the Z-score that corresponds to the 45th percentile in the standard normal distribution table. Then, we use the inverse of the Z-score formula, which is X = Z* σ + μ, to calculate the actual rent value.
Calculating the Z-score for $700:
- Z = ($700 - $735) / $55
- Z = -0.6364 (approximately)
Looking at the Z-table, a Z-score of -0.6364 corresponds to approximately 26.21%. Therefore, 26.21% of students pay less than $700 for rent.
Finding the 45th percentile value:
- The Z-score for the 45th percentile is -0.1257 (approximately).
- X = -0.1257 * $55 + $735
- X = $728.08 (approximately)
The rent value at the 45th percentile is approximately $728.08.