cannot use Minitab!! A machine produces metal pieces that are cylindrical in sha
ID: 3126479 • Letter: C
Question
cannot use Minitab!!
A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken, and the diameters are as follows: 1.01, 0.97,1.03,1.04, 0.99, 0.98,1.01,1.03, 0.99,1.00,1.00, 0.99, 0.98,1.01,1.02,0.99 centimeters. Assume normality. Do the following and discuss how the intervals are different and why. Compute a 99% Cl on the mean diameter Compute a 99% PI on the next diameter to be measured. Compute a 99% tolerance interval for coverage of the central 95% of the distribution of diameters.Explanation / Answer
Mean = 1.0025
Standard Deviation = .0.02
Standard Error = Standard Deviation/N
N = 16.
Standard Error = 0.005
a.) Margin of error = 2.58 * 0.005
= 0.013
Confidence Interval = [1.0025-0.013,1.0025+0.013]
= [0.9895, 1.0155]
b.) Prediction interval = [µ - z*SD, µ+z*SD]
Z for 99% for normal distribution is 2.58
99% PI = [1.0025-(2.58)*0.02, 1.0025+(2.58)*0.02 ]
= [0.9509, 1.0541]
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