# Express, algebraically or as an equation, the rela- tionship between standard scores and IQ scores and between standard scores and SAT

## Putting Chapter 6 to Work

- Explain why the IQ score is a continuous variable.
- What are the mean and the standard deviation for the distribution of IQ scores? SAT scores? Standard scores?
- Express, algebraically or as an equation, the rela- tionship between standard scores and IQ scores and between standard scores and SAT
- What standard score is 2 standard deviations above the mean? What IQ score is 2 standard deviations above the mean? What SAT score is 2 standard deviations above the mean?
- Compare the information about percentage of distri- bution shown in Figure 2 above with the empirical rule studied in Chapter 2. Explain the similarities.

- Let’s take a second look at the normally distributed IQ scores illustrated in “Intelligence ”

- How is an IQ score converted to a standard score?
- What is the standard score for an IQ score of 90? 110? 120?
- What is the standard score for an SAT score of 465? 575? 650?

Using Figure 2.2 with the empirical rule:

- What percentage of IQ scores is greater than 132
- What percentage of SAT scores is less than 700? Using Table 3 in Appendix B:
- What is the probability that an IQ score is greater than 132?
- What is the probability that an SAT score is less than 700?
- Compare your answers to parts f and g with your answers to parts d and e that used the empirical rule and Figure 2. Explain any similarities.
- What proportion of the IQ scores fall within the range of 80 to 120?
- What proportion of the IQ scores exceed 125?
- What percentage of the SAT scores are below 450?
- What percentage of the SAT scores are above 575?

What SAT score is at the 95th percentile? Explain what this means