The Modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi.
a. A random sample of 16 pencil leads yielded a sample mean of 6490. Construct a 90% confidence interval for the true mean MOR.
b. Find the sample size required to estimate the true mean MOR to within ± 100 using a 90% confidence interval.
c. What did you assume to do these analyses? How can you check these assumptions.
step-by-step explanation and solution is provided in the attachment.
Here we have
Sample Mean ( )= 6490
Standard Deviation (σ)= 250
Here we have n = 16
We will use standard normal distribution because the population standard deviation is known.
Z = ...
The solution of each part is provided step wise so that it can be easy to understand.