Final answer:
To find the 10th percentile of a normal distribution, locate the value corresponding to a cumulative probability of 0.10 using a z-table, calculator, or statistical software. Then, if necessary, convert this z-score to your specific distribution's scale by using the distribution's mean and standard deviation.
Step-by-step explanation:
To find the 10th percentile of a normal distribution, first understand that the 10th percentile is the value below which 10 percent of the data falls. You will generally use a z-table, calculator, or software that provides the percentile based on the standard normal distribution. To find the 10th percentile, you need to look up the value that corresponds to the cumulative probability of 0.10. If you were asked to find the 90th percentile, you would look for the value associated with a cumulative probability of 0.90 because you want 90 percent of the scores below it and the remaining 10 percent above it. Applying this to the 10th percentile, you'd find the value that has 10 percent of scores below it and the remaining 90 percent above it.
Using a standard normal distribution (which has a mean of 0 and a standard deviation of 1), you can find the z-score that corresponds to the 10th percentile. Then, if necessary, convert this z-score to the scale of the distribution you are working with by using the formula: X = μ + (z)(σ), where μ is the mean of the distribution, σ is the standard deviation, and z is the z-score corresponding to the 10th percentile.