Answer :
Final answer:
To find the score that separates the bottom 8% from the top 92%, we can calculate the corresponding z-score and then solve for the score using the formula. The score is approximately 120.2.
Explanation:
To find the score that separates the bottom 8% from the top 92%, we need to find the z-score corresponding to the 8th percentile. The z-score can be calculated using the formula: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.
Using the given values, we have: z = (x - 135.7) / 38.1.
Looking up the z-score in the z-table, we find that the z-score corresponding to the 8th percentile is approximately -1.405.
Substituting this z-score back into the formula and solving for x, we get: -1.405 = (x - 135.7) / 38.1. Solving for x gives us approximately 120.2.
Therefore, the score that separates the bottom 8% from the top 92% is approximately 120.2.
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