The manufacture of a particular handmade article takes place in two stages. The time taken for the first stage, say X₁, is approximately normally distributed with a mean of 40 minutes and a standard deviation of 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 distributed. The mean (i.e. expected value)and standard deviation of the total time, say Y, to manufacture the article are

E(Y) = 55 and SD(Y) = 25

E(Y) = 40 andSD(Y) = 5

E(Y) = 55 andSD(Y) = 5

E(Y) = 40 andSD(Y) = 25

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