A psychologist is interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of 16. The psychologist randomly selects 90 children from this group and finds that their mean IQ score is 100. Based on this sample, find a 99% confidence interval for the true mean IQ score for all children of this group. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places