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Answer: hope this helps!
Step-by-step explanation:To find P40, which represents the score separating the bottom 40% from the top 60%, we can utilize the concept of Z-scores in a normal distribution.  1. First, we need to find the Z-score corresponding to the 40th percentile. The Z-score formula is Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.  2. To find the Z-score for the 40th percentile, we look up the corresponding Z-score in a standard normal distribution table. The Z-score that corresponds to the 40th percentile is approximately -0.2533.  3. Next, we use the Z-score formula to find the raw score (P40) corresponding to the 40th percentile: -0.2533 = (P40 - 192.5) / 21.9  4. Solve for P40: P40 = -0.2533 * 21.9 + 192.5 P40 ≈ 187.1  Therefore, the score separating the bottom 40% from the top 60% is approximately 187.1 when the distribution has a mean of 192.5 and a standard deviation of 21.9.
