The service life in kilometer of Goody tires is assumed to follow a normal distribution with a standard deviation of 5,000 km. A random sample of 25 tires yielded a mean service life of 30,000 km.  1.Find the 95% confidence interval for the true mean service life. 2. Find a 75% confidence interval for the true mean service life. 3. Calculate the widths of the intervals found in 1 and 2. How do these widths change as the confidence level decreases?

Question

The service life in kilometer of Goody tires is assumed to follow a normal distribution with a standard deviation
of 5,000 km. A random sample of 25 tires yielded a mean service life of 30,000 km. 

1.Find the 95% confidence interval for the true mean service life.

2. Find a 75% confidence interval for the true mean service life.

3. Calculate the widths of the intervals found in 1 and 2. How do these widths change as the
confidence level decreases?

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