Paper 2 · November 2022 · Normal Distribution
A new detergent is made by mixing the contents of 1 satchet of dish washing liquid, mean volume 400 ml, with 2 bottles of fabric softener, mean volume 650 ml per bottle. What is the expected total volume of the new detergent, in ml?
A1700 ml
B2100 ml
C1050 ml
D1300 ml
Explanation
E(T) = E(satchet) + 2 x E(bottle) = 400 + 2(650) = 1700 ml, since the mean of a sum of independent normal variables is the sum of their means. Forgetting to double the bottle mean gives 1050 ml, counting only the two bottles gives 1300 ml, and doubling both terms by mistake gives 2100 ml.
Derived from ZIMSEC Statistics Paper 2, November 2022, Q1