1b The Earth is structured in layers: crust, mantle, and core. Arecent study was conducted to estimate the mean depth of the uppermantle in a specific farming region in California. Twenty-six,n = 26 sample sites were selected at random from anormally distributed population of approximately N = 1598sites, and the depth of the upper mantle was measured using changesin seismic velocity and density. The sample mean was 127.5 km andthe sample standard deviation was 21.3 km. Suppose thedepth of the upper mantle is normally distributed. Find a 90%confidence interval for the true mean depth of the upper mantle inthis farming region.
- Determine the prerequisites have been met (3 pts):
- Random sample:
- n ≤ 0.05 of N:
- the population is normally distributed or n ≤ 30:
- Construct the confidence interval (4 pts):
- Interpret the confidence interval, in a statement (1 pt):
1c According to the U.S. Fire Administration, approximatelyN = 25,000 fires are caused by fire-works each year in theUnited States. Despite numerous public warnings against the use offireworks, the home property damage due to these fires is enormous.In a random sample of n = 25 fires due to fireworks, theresulting mean property damage (in dollars) was 860.75 with astandard deviation of 350.50. Assume the underlying distribution ofproperty damage due to these fires is normal. Find a 99% confidenceinterval for the true mean property damage due to a fire caused byfireworks.
- Determine the prerequisites have been met (3 pts):
- Random sample:
- n ≤ 0.05 of N:
- the population is normally distributed or n ≤ 30:
- Construct the confidence interval (4 pts):
- Interpret the confidence interval, in a statement (1 pt):
