Question

12. A standard IQ test has a normal distribution with a mean of 100 with a standard deviation of 15.

a) A score of 145 or higher on this exam is categorized in the gifted realm. What percent of people would be considered gifted? ___________

b) The people who score in the lowest 5% of the standard IQ test are considered to have “mental retardation”. What cutoff score is used to qualify for this benchmark? ___________

Answer 1

µ = 100

sd = 15

a)

                               

                                = P(Z > 3)

                                = 1 - P(Z < 3)

                                = 1 - 0.9987

                                = 0.0013

                                = 0.13%

b)

or, x = 100 - 1.645 * 15

or, x = 75.325 or 75 (approx.)