Question 1181470
Here's how to find P57:

1. **Find the z-score:** P57 represents the 57th percentile.  We need to find the z-score that corresponds to a cumulative probability of 0.57. You can use a z-table or a calculator with statistical functions (like the `norm.ppf` function in Python's `scipy.stats` library). The z-score for 0.57 is approximately 0.176.

2. **Use the z-score formula:** The z-score formula is:

   z = (x - μ) / σ

   Where:
   * z is the z-score
   * x is the value we're looking for (P57)
   * μ is the mean (199.9)
   * σ is the standard deviation (82)

3. **Solve for x (P57):**

   0.176 = (x - 199.9) / 82

   Multiply both sides by 82:

   14.432 = x - 199.9

   Add 199.9 to both sides:

   x = 214.332

Therefore, P57 ≈ 214.3320