Question 1178781
Here's how to solve this problem:

**a. What is the distribution of X?**

* X follows a normal distribution with a mean (μ) of $26,423 and a standard deviation (σ) of $7,434.
* Therefore, X ~ N(26423, 7434)

**b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than $23,012 per year.**

1.  **Calculate the z-score:**
    * z = (X - μ) / σ
    * z = (23012 - 26423) / 7434
    * z = -3411 / 7434
    * z ≈ -0.4588
    * Rounding up to 2 decimal places, z = -0.46

2.  **Find the probability:**
    * P(X < 23012) = P(z < -0.46)
    * Using a z-table or calculator, P(z < -0.46) ≈ 0.3228

**c. Find the 80th percentile for this distribution.**

1.  **Find the z-score for the 80th percentile:**
    * Using a z-table or calculator, the z-score corresponding to the 80th percentile is approximately 0.84.

2.  **Calculate the value of X:**
    * X = μ + z * σ
    * X = 26423 + 0.84 * 7434
    * X = 26423 + 6244.56
    * X = 32667.56

3.  **Round to the nearest dollar:**
    * X ≈ $32,668