The firm that manufactures ABS units in India for IMM automotive is based in Chennai. It has two manufacturing units. One manufacturing unit is located in Guindy and another in Taramani. The monthly profit earned by both manufacturing units are random. Since the two units share some common resources and processes the profit earned by each are not independent. It is estimated that the correlation between the two profits is 0.4. Also the monthly profit earned by Guindy unit is normally distributed with mean 16.5 (in thousands) and standard deviation 1.5 (in thousands). Further the Taramani unit earns monthly profit which is normally distributed with mean 17 (in thousands) and standard deviation 2 (in thousands). What is the probability that the monthly profit of Guindy unit exceeds that of the Taramani unit? Hint: Difference of two normally distributed random variable is also normal.
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