Empirical Rule The Empirical Rule applies to a normal, bell-shaped curve than is symmetrical about the mean. It states that within one standard deviation of the mean (both left-side and right-side) there is about 68% of… Empirical Rule and z-score Probability
One way to improve your ability to solve normal distribution problems is to work on recognizing what word problems are requesting you to do.
Consider the following problem statement:
In an investigation of the personality characteristics of drug dealers of a certain region, convicted drug dealers were scored on a scale that provides a quantitative measure of person’s level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) Based on the study results, it can be assumed that the scale scores for the population of convicted drug dealers of the region has a mean of 44 and a standard deviation of 7. Suppose that in a sample of 96 people from the region, the mean scale score is x̅ = 46. Is this sample likely to have been selected from the population of convicted drug dealers of the region? Explain. Consider an event with a probability less than 0.05 unlikely. (McClave, Benson, & Sincich, 2014)
Solution:
First, state the question: How unusual would it be to get a sample mean of 46 if the population mean is 44 and the population standard deviation is 7?Normal Distribution: Example Problem 1