How To Find The Value Corresponding To A Given Percentile In Normal Distribution Using Table A Or Technology

Find the value that corresponds to a given percentile in a Normal distribution using Table A or technology.

Using the percentile as area (55% will translate to .55). InvNorm (area, mean, sd) = value on graph. To find z-score using percentile (use 0 for mean and 1 for sd). InvNorm (area, mean, sd) = z-score for that percent.

To find the value that corresponds to a given percentile in a Normal distribution using Table A or technology, you need to follow the following steps:

Step 1: Identify which type of Normal distribution you have. The two types of Normal distributions are standard normal distribution and non-standard normal distribution. If you have a standard normal distribution, proceed to step 3. Otherwise, proceed to step 2.

Step 2: Standardize the variable of interest by subtracting the mean and dividing by the standard deviation. This will convert the non-standard normal distribution to a standard normal distribution.

Step 3: Look up the percentile in Table A or use technology such as a calculator or statistical software to find the corresponding z-score. For example, if the percentile is 90%, the corresponding z-score is approximately 1.28.

Step 4: If you have a standard normal distribution, the value that corresponds to the given percentile can be found by using the z-score from Step 3 and the formula X = μ + zσ, where X is the value corresponding to the given percentile, μ is the mean, σ is the standard deviation, and z is the z-score obtained in Step 3. For example, if the mean is 50 and the standard deviation is 10, and the percentile is 90%, the corresponding value would be X = 50 + 1.28(10) = 63.8.

Step 5: If you have a non-standard normal distribution, the value that corresponds to the given percentile can be found by using the formula X = μ + (percentile/100)σ, where X is the value corresponding to the given percentile, μ is the mean, σ is the standard deviation, and percentile is the value of the percentile. For example, if the mean is 50 and the standard deviation is 10, and the percentile is 90%, the corresponding value would be X = 50 + (90/100)(10) = 59.

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