IQ scores

The population's IQ scores follow the normal model, with a mean of 100 and a standard deviation of 16. Answer the following questions based on the 95% confidence intervals for three schools:

The following are the 95% confidence intervals for the three schools:

(120, 130)

(90, 110)

(80, 90)

Which confidence interval is associated with a "gifted track"?

= (120, 130) (120, 130)

Which confidence intervals apply to students from a "normal track" school?

= (90, 110) (90, 110)

Which confidence interval is associated with pupils on a "academically challenging track"?

= (80, 90) (80, 90)

Providing an explanation for the answer

For part (a), the confidence interval for a “gifted track” is (120, 130) since all the students are performing above average, that is, the lower limit of the confidence interval falls above the mean. For part (b), the confidence interval for a “regular track “is (90, 110), this is the case because the mean of population (100) is included in the interval. For part (c), the confidence interval for an “academically challenged track” is highlighted by the interval (80, 90). The upper limit for this interval is less than population mean (100), therefore, there is enough information to conclude this indicated an “academically challenged track”.