Discovering Probabilities In A Normal Distribution: A Guide To Using Table A And Technology

Find the proportion of values in a specified interval in a Normal distribution using Table A or technology.

To find a percentage between values use normalcdf(lower limit, upper limit, mean, sd) = proportion. (Can use z-score to find proportion if you set mean to 0 and sd to 1).

To find the proportion of values in a specified interval in a Normal distribution, you can use Table A or technology, such as a graphing calculator or statistical software. Here are the steps:

Using Table A:
1. Determine the mean (μ) and standard deviation (σ) of the Normal distribution.
2. Identify the lower and upper bounds of the interval.
3. Find the corresponding z-scores for the lower and upper bounds by subtracting μ from each value and dividing by σ.
4. Locate the values in the left-hand column and top row of Table A that correspond to the z-scores.
5. Find the area between the two z-scores in the table by subtracting the smaller value from the larger value. This is the proportion of values in the specified interval.

Using technology:
1. Determine the mean (μ) and standard deviation (σ) of the Normal distribution.
2. Use a graphing calculator or statistical software to plot the Normal distribution.
3. Shade the area corresponding to the specified interval on the graph.
4. Use the calculator or software to find the proportion of values in the shaded area. This may be expressed as a decimal or a percentage.

It is worth noting that in a Normal distribution, approximately 68% of values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. This can be useful in estimating proportions for intervals that are within or close to these ranges.

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