Required Data set: https://www.dropbox.com/scl/fi/fbs140enk6nbiic1u8fxf/Exam.xlsx?dl=0&rlkey=20de1v4o9sx2sw1qj9ymcc75b

Please provide step by step solution for the following:

3. Three bits of analysis: a. Suppose I draw x1, x2, x10 from X~N(mu = 10, sigma = 2). What is the probability that the average of x1..x10 is less than 11 but greater than 8? Using the dataset 'Earnings' estimate the mean earnings for the students in the summer of 2019 along with its 95% confidence interval. A PhD. class has three students in it: Alice, Bob and Chris. When I ask a question in that class, someone always answers. Alice is the first one to answer twice as often as Bob and half as often as Chris. When they answer my questions in class, Alice gets it right 80% of the time; Bob, 70% of the time and Chris, 60% of the time. If I ask a single question, how likely is it that the first answer will be correct