Understanding Normal Distribution and Standard Deviation

In psychological research, researchers often collect data that is summarized in a variety of ways to help understand trends and patterns. One of the most important concepts in statistics is the normal distribution, which describes how many of the collected data points cluster around the mean. Standard deviation plays a critical role in this context, influencing how we interpret the spread of scores in relation to the mean.

Consider a study that finds the average test score of students in a large university is 80, with a standard deviation of 10. If the scores are normally distributed, what percentage of students is expected to score between 70 and 90?