Using TI 89 to apply central limit theorem

In summary, the distribution of the sample mean can be found by using the Normal cdf function on a calculator with the bounds given by 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.
  • #1
jaejoon89
195
0
(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

---

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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  • #2
http://www.tc3.edu/instruct/sbrown/ti83/normcalc.htm
 

FAQ: Using TI 89 to apply central limit theorem

1. What is the central limit theorem?

The central limit theorem states that as the sample size of a population increases, the distribution of sample means will approach a normal distribution, regardless of the shape of the original population distribution.

2. How can I use the TI 89 to apply the central limit theorem?

The TI 89 is equipped with statistical functions that can help you calculate sample means and probabilities of a normal distribution. You can also use it to create visual representations of the distribution.

3. Can the TI 89 handle large sample sizes for the central limit theorem?

Yes, the TI 89 has a large enough memory capacity to handle very large sample sizes for the central limit theorem.

4. Is the central limit theorem applicable to all types of data?

No, the central limit theorem is most applicable to data that follows a normal distribution. However, it can also be applied to non-normal data under certain conditions.

5. How can I interpret the results of applying the central limit theorem using the TI 89?

The results will show you the calculated sample means and probabilities, as well as a visual representation of the distribution. You can use these results to make inferences about the original population and its distribution.

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