Thank you for visiting A population of values has a normal distribution with u 245 1 and o 99 8 You intend to draw a random sample of size. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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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