Final answer:
To find P15, which is the IQ score separating the bottom 15% from the top 85%, we can use the standard normal distribution table or a calculator. Since the scores are normally distributed with a mean of 100 and a standard deviation of 15, we can calculate the z-score corresponding to the bottom 15%. The IQ score separating the bottom 15% from the top 85% is approximately 84.46.
Step-by-step explanation:
To find P15, which is the IQ score separating the bottom 15% from the top 85%, we can use the standard normal distribution table or a calculator. Since the scores are normally distributed with a mean of 100 and a standard deviation of 15, we can calculate the z-score corresponding to the bottom 15%.
The z-score can be found using the formula: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (x - 100) / 15.
Using the standard normal distribution table or a calculator, we can find that the z-score for the bottom 15% is approximately -1.0364. Solving the equation for x, we get x = -1.0364 * 15 + 100 = 84.46. So, the IQ score separating the bottom 15% from the top 85% is approximately 84.46.