SOLUTION: A distribution of values is normal with a mean of 199.9 and a standard deviation of 82. Find P57, which is the score separating the bottom 57% from the top 43%. P57 = ______

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Question 1181470: A distribution of values is normal with a mean of 199.9 and a standard deviation of 82.
Find P57, which is the score separating the bottom 57% from the top 43%.
P57 = ______

Enter your answer as a number accurate to 4 decimal places.
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
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
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