Problem 2 Balls for a ball bearing are machined to a desired diameter. The obtained diameter has proven to be Normal distributed. A post-production control discards all balls that that have a deviation more than 1.5 the standard deviation from the mean value. After this control the distribution for the accepted balls will read: A 1 2 f(x)= 2ncexp[-202 (xp.)] for xu 156 Where c is the standard deviation for the ball population before the control and associated discarding. a) How large fraction of the balls will be accepted? b) Make a sketch of the PDF for the uncontrolled balls and controlled balls. The controlled balls will have a truncated distribution where the tails outside 1.50 have disappeared. Inside the truncations the original distribution must be multiplied by a constant A to get the truncated distribution. Determine the value of the constant A c) How large fraction of the accepted balls will have a diameter between m-c and m+c? (Hint: to solve this problem, numerical integration is needed, and you may want to use Appendix C in the reference book)