Paper 1 · normal distribution
The volume of dish washing liquid in a satchet is normally distributed with mean 400 ml and standard deviation 45 ml. The volume of fabric softener in a bottle is normally distributed with mean 650 ml and standard deviation 50 ml, independently of the satchets. Find the probability that the total volume of 4 randomly chosen satchets is less than the total volume of 2 randomly chosen bottles.
A0.0044
B0.0228
C0.1587
D0.5000
Explanation: Let W = (sum of 2 bottles) - (sum of 4 satchets). E[W] = 2(650) - 4(400) = 1300 - 1600 = -300. Var[W] = 2(50^2) + 4(45^2) = 5000 + 8100 = 13100, so SD[W] is about 114.5. P(W > 0) = P(Z > (0-(-300))/114.5) = P(Z > 2.62), which is about 0.0044.
Derived from ZIMSEC Statistics Paper 1, November 2022, Q1
