The manufacture of a particular handmade article takes plaoe in two stages, The time taken for the rst stage, say X1 , is approximately normally distiibuted with a mean of 40 minutes and a standard deVIation 0f 3 minutes. The time taken for the second stage, say X2, is also approximately normally distributed, but with a mean of 15 minutes and a standard deVIation of 4 minutes The times to complete the two stages of production are independently distn'buted. The mean (i.e. expected value) and standard deviation of the total time, say Y, to manufacture the article are 0 Em: 55 and 50m: 25 O em: 40 and 3.000: 5 O em: 55 and 30m: 5 0 em = 40 and 30m = 25 QUESTION 4 Again referring to the probability distribution information of Question (3), the probability of nishing an article in less than 47.5 minutes is approximately (Hint: Note that the sum of two normally distributed random variables is also normally distributed) 0 0.0668 0 0.4332 0 0.9332 0 0.1587