Question

The manager of a manufacturing plant claims that the average diameter of a particular product is 5.0 millimeters. A quality inspector, however, will not accept more than 5 parts out of 1000 to have diameter 5±0.027 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each. It is known that the population standard deviation is σ = 0.1 millimeter. Based on the sample information, how many parts per 1000 are likely to have diameter 5±0.027 millimeters?

Answer 1

Level of Significance ,    α =    0.008
degree of freedom=   DF=n-1=   99          
't value='   tα/2=   2.6646   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   0.1000   / √   100   =   0.010000
margin of error , E=t*SE =   2.6646   *   0.01000   =   0.027

= 0.027

Parts likely = 8 parts of 1000

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