Question

Sammy is a translator. Based on the past record, she concludes that the time it takes her to translate an English article with 1000 words to Chinese is normally distributed with mean 120 minutes and standard deviation 9 minutes. Sammy is responsible to translate the English article to Chinese while Mary, Sammy’s colleague, is responsible to translate the English article to French. Assume Mary’s translation speed for an English article with 1000 words is another normal distribution with mean 140 minutes and standard deviation 8 minutes. It is reasonable to assume that the translation times between Sammy and Mary are independent.

(a) Find the (i) mean, (ii) variance and (iii) standard deviation of the total translation time to finish translating a 1000 words English article to Chinese and French. (5 marks)

(b) There is 4.85% chance that the total translation time is less than k minutes. What is the value of k? (5 marks)

Answer 1

Pago No. Ota - az lett be the s.ammy is time to translode د کلموديلهيه الهندلع. نحفطكليعصعصما۔ chinese - Therefore xu NC 120,81 Let y be the Mary is time to translate an English article with loca words to french. L Y UN(140, 64) _ let z be the total translation time to tinish translating a 1000 words | English article to chinese and French . ... 2 x + y since x s r are independent Therefore zu AC 2017 xt/2., 62 to 3 2 2 z n n N (120+140 81+ 64 1 N 260, 145) time ! Mean of i.e. 2 is Eczo N122 sd czy total translation exper mean of a - 260 = 145 = 1145 : 12.0415

Pago No.: YOUVA Dato: L We have given that There is 4.851. I chance that the total translation time Lis less than_k minutes. lie. Plzck] = 0.0485 => Plz-260 L 12 :04 k -200] = 0.0485 12:04 o 22fzs K - 260 7 = 0.0485_ 12.04 from normal probability calculator, We get, PIZ < -1.660 =0.0485 Comparing of | ELK - 2002 -1.660 12.04 1.660 * 12.04 +260 2400136 Ics Scanned with CamScanner