Probability & Central Limit Theorem

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Discussion Overview

The discussion revolves around the application of the Central Limit Theorem in calculating probabilities related to sample means. Participants are addressing a specific problem involving the population mean, standard deviation, and sample size, with a focus on determining the probability of a sample mean being within a certain range and whether a given sample mean is unusual.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving a population mean (μ = 12,749) and standard deviation (σ = 1.2) with a sample size (n = 35), asking for the probability of a sample mean being less than 12,749 or greater than 12,752.
  • Another participant emphasizes the importance of showing progress in problem-solving to facilitate better assistance, requesting the original poster to share their work thus far.
  • A participant calculates the standard error of the mean (σx = 0.2028) and attempts to compute the z-score but expresses confusion about the arithmetic involved in the calculation.
  • There is a question raised regarding the correct formulation of the z-score calculation, highlighting a potential misunderstanding in the order of operations or the expression used.
  • One participant suggests that the original poster should perform the arithmetic and utilize a normal distribution table or application for further assistance.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct approach to the z-score calculation, and there is confusion expressed regarding the arithmetic involved. The discussion remains unresolved with multiple viewpoints on how to proceed.

Contextual Notes

There are limitations in the clarity of the z-score calculation and the assumptions made about the normal distribution. The discussion does not resolve these mathematical steps.

rihnavy
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The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.
μx̄ = μ = 12,749
σ = 1.2
n = 35

For the given sample n = 35, the probability of a sample mean being less than 12,749 or greater than 12,752 is ____________

 
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Hello rihnavy :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
This is what I have so far.
σx = σ/ √n = 1.2/ √35 = 0.2028

z = x̄ - μx̄/σx = x̄ - μx̄/σ/√n = 12,749 - 12,752/ 1.2√35 = -0.4226 = .33724

I stopped right there because I got confused. I'm stuck.
OTE=greg1313;90547]Hello rihnavy :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?[/QUOTE]
 
rihnavy said:
This is what I have so far.
σx = σ/ √n = 1.2/ √35 = 0.2028

z = x̄ - μx̄/σx = x̄ - μx̄/σ/√n = 12,749 - 12,752/ 1.2√35 = -0.4226 = .33724
Do you mean 12,749- (12,752/1.2√35) (which is what you wrote means) or do you really mean
(12,749- 12,752)/1.2√35?

I stopped right there because I got confused. I'm stuck.
Could you not at least do that arithmetic? Do you not have a table of the Normal distribution or an app that gives them?
 

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