A manufacturer of automobile batteries is concerned about the life of the batteries that are produced. The manufacturer is comfortable with the average life of the batteries but more concerned about the standard deviation. Research has shown that the average life of the automobile batteries is 55 months. However, the manufacturer would like the standard deviation of the life of the automobile batteries to be relatively small, say, approximately nine months. To determine a reliable range of the standard deviation of the batteries currently being produced, the manufacturer took a random sample of 20 batteries and found that the average life was 58 months with a standard deviation of eight months. Assuming that the life of batteries produced by the automobile manufacturer has an approximately normal distribution, construct an 80% confidence interval for the standard deviation of the life of their automobile batteries. Round any intermediate calculations to no less than six decimal places and round the endpoints of the interval to four decimal places.