Question

Lazurus Steel Corporation produces iron rods that are supposed to be inches long. The machine that makes these rods does not produce each rod exactly inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is inches. The standard deviation of the lengths of all rods produced on this machine is always equal to inch. The quality control department takes a sample of such rods every week, calculates the mean length of these rods, and makes a confidence interval for the population mean. If either the upper limit of this confidence interval is greater than inches or the lower limit of this confidence interval is less than inches, the machine is stopped and adjusted. A recent sample of rods produced a mean length of inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such rods have a normal distribution. Round your answers to two decimal places. The confidence interval is _ to _inches.

Answer 1

Since you have provided data

I am going to give formula with an example

Assuming sample mean is 36.015

sd = 0.035

n = 20

assuming alpha = 0.05 , z = 1.96

confidence interval is

36<μ<36.03

if alpha = 0.10 , z = 1.645

36.002<μ<36.028