Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches l
ID: 3175611 • Letter: L
Question
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rodes does not produce each rod exactly 36 inches long; the length 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 36 inches. The standard deviation of the lenghts of all the rods produced on this machine is always equal to .10 inch. The quality control department takes a random sample of 20 such rods every week, calculates the mean lenghts of these rods, and makes a 99% confindence interval for the population mean. if either the upper limit of this confidence interval is greater than 36.05 inches or the lower limit of this confidence interval is less than 35.95 inches, the machine is stopped amd adjusted. A recent sample of 20 rods produced a mean length of 36.02 inches. Based on this sample will you conclude that this machine needs an adjustment? Assume that the lengths off all such rods have an approximate normal distribution.
Explanation / Answer
n = 20
x-bar = 36.02
s = 0.1
% = 99
Standard Error, SE = /n = 0.1 /20 = 0.02236068
z- score = 2.575829304
Width of the confidence interval = z * SE = 2.57582930354892 * 0.0223606797749979 = 0.057597294
Lower Limit of the confidence interval = x-bar - width = 36.02 - 0.0575972942117132 = 35.96240271
Upper Limit of the confidence interval = x-bar + width = 36.02 + 0.0575972942117132 = 36.07759729
The upper limit of the confidence interval is greater than 36.05. This means the machine needs an adjustment.
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