Probability & Central Limit Theorem

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SUMMARY

The discussion centers on calculating the probability of a sample mean using the Central Limit Theorem with a population mean (μ) of 12,749, a standard deviation (σ) of 1.2, and a sample size (n) of 35. The user calculated the standard error (σx) as 0.2028 and attempted to compute the z-score, resulting in a value of -0.4226. The conversation emphasizes the importance of showing progress when seeking help to facilitate effective assistance.

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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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