Question 1181519
Here's how to calculate these probabilities:

**1. Probability for a single randomly selected value (X):**

*   We're looking for P(X > 17.6).
*   First, calculate the z-score:  z = (X - μ) / σ = (17.6 - 18) / 3.2 = -0.125
*   Now, look up the probability associated with this z-score in a standard normal distribution table or use a calculator.  P(Z > -0.125) = 1 - P(Z < -0.125) ≈ 1-0.4503 = 0.5497

**2. Probability for a sample mean (M):**

*   We're looking for P(M > 17.6).
*   The standard error of the mean is: σ_M = σ / sqrt(n) = 3.2 / sqrt(73) ≈ 0.374
*   Calculate the z-score for the sample mean: z = (M - μ) / σ_M = (17.6 - 18) / 0.374 ≈ -1.069
*   Now, look up the probability associated with this z-score. P(Z > -1.069) = 1 - P(Z < -1.069) ≈ 1 - 0.1423= 0.8577

**Therefore:**

*   P(X > 17.6) ≈ 0.5497
*   P(M > 17.6) ≈ 0.8577