Question

Problem 3 - The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceeding 10.634 ohms, and 5% having a resistance smaller than 9.7565 ohms. What are the mean value and standard deviation of the resistance distribution?

Answer 1

let x resistance of resistor 104. of all resistor having resistance Borallo enceeding 10.634 chn o P (x >10.634) = 0.10 P(x-4 10.634-4)=0.10 2 where. ll- pop. mean = E(X) o-sd-of x = 5d(x) op (23 10.634-1=0010 from standard normal table P a y Zai) = 0.10 -> 2c, = 1.282 ze = 10.634-4 = 1.282 10.634 - l = 1.282 0 - 0 57. haring a resistance smaller than 9.75os ohns. ie P(x29.7565)=0.05 Pex-42 9.7565-) -0.05 P(Z < 9.7565 =0.05 also P(Z <Z) = 0.05 > 2= -1.645 - Zen 9.7565-M = -1.645 => 9.7565 - u=-1.645 T solving Û f ③ T = 0.2998 M = 10.2497 mean = 102497 sd 0.2998 x -> N(10.2497, 730.2998')