Question

Some IQ test are standardized to a normal model, with a mean of 100 and a standard deviation of 15

(a) in what interval would you expect the central 95% of IQ scores to be found
(b) About what percent should have IQscores above 115
(c) About what percent of people should have IQ scores between 70 & 85
(d) About what percent should have IQ scores above 130%

Answer 1

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Explanation: