The average life of a certain type of motor is 10 years with astandard deviation of 2 years. You are interested in measuring thelife time of this motor by conducting a survey asking customers’experiences. Use this information and answer Question 4a to 4h.
Question 4a: What is the probabilitydistribution of the life time of the motor, X?
Question 4b: In the first week, you were ableto obtain 25 survey responses on the life of the motor you arestudying. What is distribution of the average life of the motor, XĂ‚ÂŻ?
Question 4c: After a month-long survey, youcollected 367 responses. What would be the expected value of theaverage life time of the motor using the survey responses?
Question 4d: After a month-long survey, youcollect 367 responses. What is the probability that the averagelife time of the motor is greater than 10 years and 3 months? (Usefour decimal places)
Question 4e: After a month-long survey, youcollect 146 responses and find that the average life of the motoris 10.02 years. What is the upper limit of a two-sided 95%confidence interval of the true average life of the motor? (Usefour decimal places)
