AP PSYCHOLOGY

Detailed explanation-1: -Approximately 95% of the population has IQ scores between 70 and 130. Approximately 99.7% of the population has IQ scores between 55 and 145.

Detailed explanation-2: -The Empirical Rule or 68-95-99.7% Rule can give us a good starting point. This rule tells us that around 68% of the data will fall within one standard deviation of the mean; around 95% will fall within two standard deviations of the mean; and 99.7% will fall within three standard deviations of the mean.

Detailed explanation-3: -If we wanted to specify the middle 95% of a normal distribution, then the magical number is 1.96: 95% of the probability mass in a normal distribution falls within 1.96 standard deviations on either side of it.

Detailed explanation-4: -A 95% confidence interval for the standard normal distribution, then, is the interval (-1.96, 1.96), since 95% of the area under the curve falls within this interval.

Detailed explanation-5: -For example, given that the IQ scores have a mean of 100 and a standard deviation of 15, one can conclude that only about 2.3% of the population have an IQ of 130 or higher.