Using TI 89 to apply central limit theorem

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To apply the Central Limit Theorem using a TI-89 calculator, the discussion highlights the need to find the distribution of the sample mean. The formula provided relates the standardized variable Z to the sample mean and population parameters. Users express uncertainty about using the Normal cumulative distribution function (cdf) due to unclear bounds. The TI-89 can simplify the process, as solving the integral analytically is complex. Clarifying the bounds for the Normal cdf is essential for accurate calculations.
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(to find distribution of sample mean)

Given

P((X1 - μ) / σ/√n) < Z < (X2 - μ) / σ/√n)) = P(a < Z < b) = phi(b) - phi(a)

where phi(z) = 1/sqrt(2*pi) * integral of exp(-z^2 / 2) dz from negative infinity to z

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I'm sure there's some statistical way of doing this with a TI 89, but how? The Normal cdf asks me for bounds, which I don't see what they would be here. so I figure that is not the correct function on the calculator. Using the calculator would be helpful since it's obviously not easy to solve this integral analytically.
 
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http://www.tc3.edu/instruct/sbrown/ti83/normcalc.htm
 
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