In your state, possible scores on the written part of the driver's license exam range from 0 to 20. The department's records indicate that the mean score on this test is 11.2, and that the scores are roughly normally distributed. They do not keep information on the standard deviation of scores on the test. A random sample of 12 applicants are given a new experimental version of the preparation booklet to study before taking the test. After studying the new version, they each take the test. Their scores are given below.

X = 10 7 17 12 20 15 14 8 12 16 19 11

a) Estimate the mean and variance for the new version of the booklet (i.e. calculate Xbar and s^2)

b) Using the t distribution, construct a 95% C.I. for the mean of people studying the new booklet.

c) Test (at .05) if the mean score of applicants using the new booklet is different than 11.2.

Please help me solve parts a. b, and c of this question. I'd appreciate a step-by-step explanations. Also, this was the information provided by my instructor. Thank you!