Question

An automatic turning machine produces rods of eqaal diameters of 200 mm. For acceptable diameter, it should not deviate from 200 mm by more than about 1%. One hundred diameters was measured during the machine production. The resulting data are tabulated below. The resolution of digital micrometer is 001 mm. the measured diameters shown below are grouped for intervals 0.25 mm centered about the listed diameter. x (diam. mm) 198.5 199 202 202.5 199.5 200 200.5 201.0 201.5 Frequency 1 1 2 3 2 25 6 17 33 5.4a Plot the histogram of the measured diameters, determine mean diameter and the standard deviation. Is the distribution Gaussian? 3 Fmen

Answer 1

Histgram 33 gb 30 8 T 5 12 C 94 dia 198.5 201 s'loc 202 202.5

98.5 19+199.5+200+200.5+ 20l. O Mean diameler 11 + 201. 5 202+ 2o2.5 Mean diameter 200.5 Ans For standard devialion X ニ 20の.5 class Mid Value Cx) Bouent any (f) Devialion d=x-文 fxd2 fxd 4 198.25-198.7s 148.5 -2 -.5 148.75-199.25 12 -12 99.25 -199.75 199. 5 G. 25 o.5 -12.5 25 200 l99.75 -20o. 25 3Z 200.25-200.S 20O.5 425 8.5 D.S 200.15-201.25201.o 201.25-20/.75 201.S 4.5 3 201-75-202.25202.o 2 2 202.25-2o275202-5 Zfxd2 ニ47-75 |Efxd ニ-|-5

stindared Devialion Sf 47.7.5 -I1.5 O. G8 Ans To check Por Graussian (Noma|) Distibution B Popertres Completely deseribed hy Population standard deviation Papulation the meah for distriaulion tbe normal about shuld lie bitween 68 Valus 10 S.D 10 mon 10

68 6. 12 for 9 Values but than 6 Valluas Not more beth 1o mean 16 E 200. S- xO.68 199.82 mean l5 200.5t 1X0.68 201. 18 Range is 199.82 201. 18 or 10 het this range but 3 Values Lies For oabout beth q5 Values eshauld 1ie 2 6 -20 The distribution is hot Gaussian