Are the NAEP U.S. history scores approximately Normal? In Exercise 1.113, we assumed that the NAEP U.S. history scores for twelfth-grade students are approximately Normal with the reported mean and standard deviation, N(288, 32). Lets check that assumption. In addition to means and standard deviations, you can find selected percentiles for the NAEP assessments (see previous exercise). For the twelfth-grade U.S. historyscores, the following percentiles are reported:Percentile Score10% 24625% 27650% 29075% 31190% 328Use these percentiles to assess whether or not the NAEPU.S. history scores for twelfth-grade students are approximatelyNormal. Write a short report describing yourmethods and conclusions.

3.1 Ans12) (a) Mean = Sum of all values divided by the number of values. Mean = ∑ x /n = 23/5 = 4.6 In order to calculate the median, we arrange the set of numbers in increasing order: 2 2 3 6 10. As the number of observations are odd, therefore median is the third value which is 3. Median = 3. Mode is the number that occurs most frequently in the given data. In this case, 2 occurs most frequently. So, mode is 2. (b)As per the question, we add 5 to each of the data values. New data set: 7 7 8 11 15. Mean = ∑ x /n = 48/5 = 9.6 In order to calculate the median, we arrange the set of numbers in increasing order: 7 7 8 11 15. As the number of observations are odd, median is the middle value which is the third value in this case. Median = 8. Mode is the number that occurs mos