# Sammy is a translator. Based on the past record, she concludes that the time it takes her to Q4. translate an English article….

**Question:**

Sammy is a translator. Based on the past record, she concludes that the time it takes her to Q4. 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. 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. (a) (5 marks) There is 4.85% chance that the total translation time is less than k minutes. What is the value (5 marks) (Total: 10 marks) (b) of k?

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