Problem: IQ scores are generally normally distributed, with a mean of 100 and a standard deviation of 16. Find:
A. Percentage of scores less than 100.
B. Percentage of scores less than 84.
C. Percentage of scores greater than 116.
D. Percentage of scores less than 76.
E. Percentage of scores greater than 132.
F. Percentage of scores less than 80.
G. Percentage of scores less than 65.
H. Percentage of scores less than 129.
I. Percentage of scores between 84 and 116.
J. Percentage of scores between 76 and 124.
K. Percentage of scores between 80 and 120.
L. Percentage of scores between 92 and 115.
2- In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. He gave each surveyed person two scenarios, and they had to choose one option in each.
Scenario 1: You have a choice of (A) a 100% chance of gaining $1 million, or (B) a 10% chance of gaining $2.5 million, a 89% chance of gaining $1 million and a 1% chance of gaining nothing.
Scenario 2: You have a choice of (A) an 11% chance of gaining $1 million and a 89% chance of gaining nothing, or (B) a 10% chance of gaining $2.5 million and a 90% chance of gaining nothing.
Allais discovered that for Scenario 1, most people choose A, while for Scenario 2, most people choose B.
For each decision, find the expected value of each scenario. Are the responses given by the survey participants consistent with the expected values? Explain.