Probability (Normal population distribution)

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Discussion Overview

The discussion revolves around a probability problem involving two samples of apples drawn from normal population distributions. Participants explore the concept of sampling distributions and the central limit theorem as they relate to comparing the means of the two samples.

Discussion Character

  • Homework-related, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant presents a probability question involving the comparison of sampling means from two different populations.
  • Another participant prompts for understanding of the sampling distributions of the two means, suggesting that knowledge of this concept is necessary to solve the problem.
  • A different participant expresses confusion regarding the term "sampling distribution information" and seeks clarification on its relevance to the original question.
  • Another participant emphasizes the need for the original poster to demonstrate prior engagement with the material, such as referencing the central limit theorem or sampling distributions, before receiving assistance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the understanding of sampling distributions, with some expressing confusion and others insisting on the necessity of this knowledge for solving the problem.

Contextual Notes

Participants highlight the importance of prior knowledge regarding sampling distributions and the central limit theorem, but the specific assumptions or definitions related to these concepts remain unresolved.

yyh1
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Can anyone help me to solve this question:

A random sample of twenty-five apples is obtained from a normal population distribution with a mean of 80 grams and a standard deviation of 5 grams. Another random sample of 36 apples is obtained from a population distribution having a mean of 75 grams and a standard deviation of 3 grams. Find the probability that the sampling mean from the first sample is bigger than the sampling mean from the second sample with at least 3.4 grams but less than 5.9 grams.
 
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Interesting. What do you know about the sampling distributions of the two means?
 
statdad said:
Interesting. What do you know about the sampling distributions of the two means?

Hmm.. no idea.. If u know the answer for this question, kindly explain to me.. thx
 
the information you need should be in the material you've learned about normal distributions. look in your notes/text for "sampling distribution" or "central limit theorem" - once you have the sampling distribution information, post again.
 
I do not get what do u mean by "sampling distribution information", the question is exactly what I written there..
 
I believe the question is as you posed: it refers to the 'sampling mean' in two locations. That is the quantity to which I referred: if you have this problem to solve, you should have seen something that used that term, or central limit theorem, or sampling distribution.
You need to provide some evidence of working on this before you get help.
 

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