Question

Resistances. An automat produces resistors whose experience has shown that they are realizations of a normally distributed random variable with µ = 1000 Ω and σ = 20 Ω. Resistances outside the tolerance limits of 960 Ω and 1050 Ω count as rejects.
1. How many of 950 resistors are on the middle committee?
2. The proportion of resistors with a value greater than 1050 Ω should be reduced to an average of 0.1%. How large must µ be if the mean square deviation σ 2 remains unchanged?

Answer 1

99.997, Given 95.95% ll=1000 20 ř 20 3r. -30 -20 - U-1008 R = " +20, Mir u+3r. iie are R blw er to ear ie 980 to 1020 68.67% R b/w u-ar to utar ie 960 to 1040 are 95.95% ire R blw 4-30 to M435 quo to 1060 are 99.994. is There are nearly nay of total resistance of ale Present in 950 a Resistance 27 R 7 1050 should reduced to 0.1% a velge ltr = loso M +20 = 1050 M = 1030 > Therefore resistance should increase to 1030 from 1000.