Q:

The Stanford-Binet IQ scale is normally distributed, with random normal variable X ~ N(100, 15). For this problem, consider the following IQ scores: 82, 96, 100, 104, 118 (Round your answers to 4 decimal places unless otherwise instructed.) a. Draw a normal curve, and be sure to:

1. indicate (approximately) where , +, +2, - and -2 fall on the x-axis. 2. indicate (approximately) where each of the IQ scores above fall on the x-axis.

b. For each IQ score above:

1. Convert the IQ score into its corresponding z-score. (Round your z-scores to 2 decimal places.) 2. what is P(X < IQ)? 3. what is P(X > IQ)? 4. If the IQ score is less than , what is P(IQ < X < )? 5. If the IQ score is greater than , what is P( < X < IQ)? ~Find the following probabilities. (Round your final answers to 3 decimal places.) 6. P(z < -1.96) 7. P(z > 1.96) 8. P(z < -1.65) 9. P(z > 1.65) 10. P(z < -2.33) 11. P(z > 2.33) 12. P(z < -2.58) 13. P(z > 2.58)