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