Mastering Normal Distribution: A Step-By-Step Guide To Finding Proportions In A Specified Interval Using Table A Or 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 using Table A or technology, follow these steps:

1. Determine the parameters of the Normal distribution. These include the mean and standard deviation.

2. Decide on the interval of interest, which can be defined by its lower and upper bounds.

3. Convert the lower and upper bounds of the interval to their corresponding Z-scores, which describe how many standard deviations away from the mean each bound is. To compute these Z-scores, you can use the formula:

Z-score = (x – μ) / σ

where x is the value of the lower or upper bound, μ is the mean, and σ is the standard deviation.

4. Use Table A or a statistical calculator to determine the area under the Normal curve between the two Z-scores computed in step 3. Table A provides probabilities for the standard Normal distribution, where the mean is zero and the standard deviation is 1. Locate the closest Z-scores to the ones calculated in step 3 and find the corresponding probability. For example, if the lower bound has a Z-score of -1.85 and the upper bound has a Z-score of 2.42, find the probability between -1.85 and 2.42 in Table A. Alternatively, you can use a statistical calculator to compute the probability directly, using the mean and standard deviation of the distribution.

5. The proportion of values in the specified interval is equal to the probability found in step 4.

It is important to note that when using Table A, you may need to interpolate between rows or columns to find the exact probability corresponding to the calculated Z-scores. Additionally, if the distribution is not standard Normal, you may need to use a software program or statistical calculator that allows you to input the mean and standard deviation of the distribution to compute probabilities.

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