Question

You are working part-time at a road construction firm. your boss knows you are learning some statistics in your classes this semester and calls you into the office. he says, "we've taken sample densities from loads of asphalt we've gotten from our supplier. the information from their company says their process produces a consistent density with a standard deviation of 2.65 pounds per cubic foot. here's the data we've collected. can you give me an estimate of the average density that our supplier's process is producing? i want to be 80% confident of the range you provide."

Answer 1

Missing data can found here https://www.dropbox.com/s/u5t2sjj7pglu7iw/CIData%20%281%29.txt?dl=0
The first step is to calculate the mean of the data provided.
$\mu=\frac{a_1+a_2+a_3\cdots a_k}{k}$
k is a number of points in our data set. 
The mean for our data set is $\mu=145.80$.
Now we need to find the range associated with confidence level required.
Z score associated with a confidence level of 80% percent is 1.28. 
We know that our range has to be $z\cdot\delta$ in order for us to be 80% confident in our result. As the confidence level rises z score associated with it also rises. This makes sense because the broader your range is more confident you are that measurement will fall within that range.
The final answer would be:
$\rho=\mu \pm z\delta=145.80 \pm 3.39$