Question

ustion 2: (Discrete Random variable)[2+2-4 marks] A factory produces components of which I % is defective. The components are in boxes of 10 A box is selected at random (a) Find the probability that the box contains at least 2 defective components. (b) Find the mean and the standard deviation of the distribution Cy e length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a) less than 7 months. b) between 7 and 12 months. uestion 3: Continuous probability distribution [2+3-5 mark

Answer 1

Consider a unit length in Z, the charge contained upto this radius l is Q = integral^1_0 integral^2 pi_0 integral^rho_0 rho_0/(p^2 + a^2) ^2 e^' dp^' d straightpidz = [2 pi rho_0] [-1/2(ho^2 + a^2)]^rho_0 [1-0] = 2 pi rho_0 [-1/2(p^2 + a^2)]^rho_ 0 pi rho_0 /a^2 We can find total charge when P rightarrow infinity Q(total) = [1 - 1/1 + rho^2/a^2] If rho - a , the above eq becomes = [1-1/1-rho^2/rho^2] = 1- 1/2 = [1 /2] so, when rho = a , the half of total charge be