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The average life of a certain type of motor is 10 years with a standard deviation...

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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, X¯?

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)

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