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, follow these steps:
1. Determine whether you are dealing with a one-tailed or two-tailed test.
2. Look up the appropriate area in the standard Normal distribution table (Table A) or use a technological tool that calculates probabilities in a normal distribution.
3. If you’re using Table A, locate the correct value for the percentile you’re interested in. The table provides the area to the left of the z-score. If the percentile you’re interested in is greater than 50%, you will need to use the symmetry of the normal distribution and find the corresponding z-score for the area to the right.
4. If you’re using technology, input the percentile you’re interested in and the program will provide you with the corresponding z-score.
5. Once you have the z-score corresponding to the desired area or percentile, use the formula z = (x – μ) / σ to solve for x, where x is the value you are trying to find, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.
More Answers:
Mastering Data Analysis: Key Steps To Describe And Summarize A Data Set With Distribution, Central Tendency, Dispersion, Relationships, And Visualization.Mastering Numerical Descriptions Of Data: A Comprehensive Guide For Statistical Analysis
Mastering Normality Assessment: Graphical And Numerical Techniques For Detecting Normal Distributions In Data