A number of years ago a friend of mine produced a diagnostic test of language problems. A score on her scale is obtained simply by counting the number of language constructions (e.g., plural,...

A number of years ago a friend of mine produced a diagnostic test of language problems. A score on her scale is obtained simply by counting the number of language constructions (e.g., plural, negative, passive) that the child produces correctly in response to specific prompts from the person administering the test. The test had a mean of 48 and a standard deviation of 7. Parents had trouble understanding the meaning of a score on this scale, and my friend wanted to convert the scores to a mean of 80 and a standard deviation of 10 (to make them more like the kinds of grades parents are used to). How could she have gone about her task?