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\nTI-83 Normal Distribution: Approximate p(x)
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Use this calculator to find the probability of a value occurring within a normal distribution using the TI-83’s Normal CDF function.
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Inputs
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How to Use This on a TI-83
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This calculator demonstrates the values you would input into the Normal CDF function on your TI-83 graphing calculator.
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| Button Sequence | Screen | Purpose |
|---|---|---|
| 2nd → VARS (DISTR) | [DISTR] Menu | Access probability distributions |
| 2 | normalcdf( | Select Normal CDF |
| lower, upper, 0, 1 | normalcdf(-5, 5, 0, 1) | Enter values (lower, upper, mean, std dev) |
| 2nd → QUIT | 2.529E-5 | View result |
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Understanding the Calculation
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The TI-83 calculates the area under the normal distribution curve between the lower and upper bounds.
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Formula:
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$$P(a \\le X \\le b) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\int_{a}^{b} e^{-\\frac{1}{2}(\\frac{x-\\mu}{\\sigma})^2} dx$$
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On the TI-83, this is simplified to: normalcdf(lower, upper, mean, stdDev)
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Practical Example: IQ Scores
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IQ scores are normally distributed with a mean ($\\mu$) of 100 and a standard deviation ($\\sigma$) of 15.
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What is the probability of scoring between 85 and 115?
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Inputs:
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- Lower: 85
- Upper: 115
- Mean: 100
- Std Dev: 15
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TI-83 Entry: normalcdf(85, 115, 100, 15)
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Result: 0.6827 (68.27%)
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Common Errors
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- Forgetting to switch to 2nd mode for DISTR
- Using probability instead of standard deviation
- Entering values in the wrong order
- Not accounting for \”tails\” in non-standard distributions
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