In a study of babies born with very low birth weights, 275 children were given IQ tests at age 8, and their scores approximated a normal distribution with µ = 95.5 and σ = 16.0 (based on data from “Neurobehavioral Outcomes of School-age Children Born Extremely Low Birth Weight or Very Preterm,” by Anderson et al., Journal of the American Medical Association, Vol. 289, No. 24). Fifty of those children are to be randomly selected for a follow-up study.
a. When considering the distribution of the mean IQ scores for samples of 50 children, should σx be corrected by using the finite population correction factor? Why or why not? What is the value of σx?
b. Find the probability that the mean IQ score of the follow-up sample is between 95 and 105.