IQ test scores are standardized to produce a normal distribution with a mean of mu = 100 and a standard deviation of sigma =15 . Find the proportion of the population in each of the following IQ

a. To find the proportion of the population with an IQ greater than 140, we need to find the area to the right of 140 on a normal distribution curve with mean 100 and standard deviation 15. We can use a standard normal table or calculator to find that this area is 0.0228 or \approx imately 2.28%. Therefore, \approx imately 2.28% of the population would be classified as having genius or near genius intelligence. b. To find the proportion of the population with an IQ between 120 and 140, we need to find the area between 120 and 140 on a normal distribution curve with mean 100 and standard deviation 15. We can use a standard normal table or calculator to find that this area is 0.1359 or \approx imately 13.59%. Therefore, \approx imately 13.59% of the population would fall under the category of very superior intelligence. c. To find the proportion of the population with an IQ between 90 and 109, we need to find the area between 90 and 109 on a normal distribution curve with mean 100 and standard deviation 15. We can use a standard normal table or calculator to find that this area is 0.3830 or \approx imately 38.30%. Therefore, \approx imately 38.30% of the population would be classified as having average or normal intelligence.