Answer to Question #119496 in Statistics and Probability for Mia

Question

Is the following statement sometimes, always or never true? If they are only true give examples or conditions under which they are true and under which they are false.
1. Half of the students taking a test score less than the average mark.

Answer 1

The normal distribution is most familiar and useful in describing the frequency of standardized test scores, how many students earned particular scores. The mean of the normal distribution divides the curve in half, so that 50% of the area under the curveis to the right of the mean and 50% is to the left. Therefore, 50% of testscores are greater than the mean, and 50% of test scores are less than the mean. Of course not all test score distributions are normally distributed. They can be skewed, i.e. have a disproportionate number of people who dovery well or very poorly. This would be the case if a test was too easy or too hard for the testing population. However, standardized tests are designed so that the outcome follows a normal distribution curve. So when it is a normal distribution - it is always true