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Answer :
Final answer:
The value separating the bottom 82% of values from the top 18% is 336.5 and the sample mean separating the bottom 82% of sample means from the top 18% is 251.1, both to one decimal place.
Explanation:
To answer this question, we'll use a statistical concept called a Z-score. A Z-score represents how many standard deviations a given data point is from the mean. In a normal distribution, the bottom 82% is cut off at a Z-score of 0.915.
To find the value separating the bottom 82% values from the top 18%, we will use the formula: Value = μ + σ * Z-score. So Value = 245.1 + 99.8*0.915 = 336.5 to one decimal place.
Then, to find the sample mean separating the bottom 82% sample means from the top 18% sample means, we'll use the Standard Error of the mean formula which is σ / √n. Applying the formula we get, 99.8 / √232 = 6.6 to one decimal place.
Following the same methodology as before using the Z score and standard error: Sample Mean = μ + (Standard Error * Z-score). So Sample Mean = 245.1 + 6.6*0.915 = 251.1 to one decimal place.
Learn more about Z-score here:
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