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Answer :
Final answer:
To find the sample mean associated with the bottom 20% of a normally distributed population, apply the Central Limit Theorem to determine the standard error and utilize the z-score for the 20th percentile. None of the option are correct.
Explanation:
The question falls under the subject of Mathematics and applies to a College level understanding of statistics, specifically the concept of the sampling distribution of the sample mean. When considering a random sample of n = 25 from a normal distribution with μ = 100 and σ = 15, we look to identify the sample mean corresponding to the bottom 20% of this distribution.
To do so, we apply the Central Limit Theorem which indicates that the sampling distribution of the sample mean will also be normally distributed with the same mean μ = 100 but with a reduced standard deviation (standard error) equal to rac{σ}{ext{√}n}=rac{15}{ext{√}25} = 3.
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