# 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.
1. What are the mean and the standard deviation for the distribution of IQ scores? SAT scores? Standard scores?
2. Express, algebraically or as an equation, the rela- tionship between standard scores and IQ scores and between standard scores and SAT
3. 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?
4. 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 ”
1. How is an IQ score converted to a standard score?
2. What is the standard score for an IQ score of 90? 110? 120?
3. What is the standard score for an SAT score of 465? 575? 650?

Using Figure 2.2 with the empirical  rule:

1. What percentage of IQ scores is greater than 132
2. What percentage of SAT scores is less than 700? Using Table 3 in Appendix B:
3. What is the probability that an IQ score is greater than 132?
4. What is the probability that an SAT score is less than 700?
5. 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.
6. What proportion of the IQ scores fall within the range of 80 to 120?
7. What proportion of the IQ scores exceed 125?
8. What percentage of the SAT scores are below 450?
9. What percentage of the SAT scores are above 575?

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

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