IQ tests have been used for more than a century to try to measure human intelligence. (They were originally intended to identify children who needed special education.) When an IQ test is developed, a sample representing the general population is given the test. The median score in the sample is set equal to 100 IQ points and standard deviation is commonly set equal to 15. When a new test-taker takes the test, he/she is assigned an IQ score equal to the IQ score for sample members who had the same test result. For large groups, IQ scores have a normal distribution.
a. Given such a test, what percentage of the population will have an IQ score less than 75?
b. What percentage will have an IQ score greater than 120?
c. 80% of the population will have an IQ greater than____.
d. 25% of the population will have an IQ between 105 and_____. Make 105 the lower bound for your interval.