Paper 1 · normal distribution
A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than 1.95 kg. Find the standard deviation of the packet weights, correct to 3 decimal places (in kg).
Model answer
0.039
Also accepted: 0.0390, 0.039 kg
Explanation: P(X < 1.95) = 0.10 corresponds to a z-value of -1.2816 (from tables). Since z = (1.95-2)/sigma, -0.05/sigma = -1.2816, so sigma = 0.05/1.2816, which is about 0.039 kg.
Derived from ZIMSEC Statistics Paper 1, November 2022, Q2
