MHB Probability & Central Limit Theorem

AI Thread Summary
The discussion focuses on calculating the probability of a sample mean being less than 12,749 or greater than 12,752, given a population mean (μ) of 12,749, a standard deviation (σ) of 1.2, and a sample size (n) of 35. A user has calculated the standard error (σx) as 0.2028 and attempted to find the z-score but is confused about the arithmetic involved. Clarification is sought on the correct formula to use for the z-score calculation. The conversation emphasizes the importance of sharing progress to receive effective assistance. Understanding the Central Limit Theorem is crucial for determining the unusual nature of the sample mean.
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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