The Earth is structured in layers: crust, mantle, and core. A recent study was conducted to estimate the mean depth of the upper mantle in a specific farming region in California. Twenty-six sample...

The Earth is structured in layers: crust, mantle, and core. A recent study was conducted to estimate the mean depth of the upper mantle in a specific farming region in California. Twenty-six sample sites were selected at random, and the depth to the upper mantle was measured using changes in seismic velocity and density. The summary statistics are x 5 127.5 km and s 5 21.3 km. Suppose the depth of the upper mantle is normally distributed. Find a 95% confidence interval for the true mean depth of the upper mantle in this farming region, and interpret your result.

In many rural areas, newspaper carriers deliver morning papers using their automobiles because the length of the route prohibits walking. In a random sample of 28 carriers who use their automobiles, the sample mean route length was x 5 16.7 miles with s 5 3.4.

a. If the ditribution of route lengths is normal, find a 95% confidence interval for the true mean route length of newspaper carriers who use their automobiles.

 b. If the mean length of the routes is over 20 miles, the circulation department becomes concerned that papers will not be delivered by 7:00 a.m. Using your answer to part (a), is there any evidence to suggest the true mean route length is over 20 miles? Justify your answer. Write a Solution Trail for this problem.