Paper 2 · 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. What is the standard deviation of the packet weights, in kg (to 3 decimal places)?
A0.025 kg
B0.030 kg
C0.039 kg
D0.064 kg
Explanation: P(X < 1.95) = 0.10 corresponds to a standard normal value of z = -1.2816. Since (1.95 - 2)/sigma = -1.2816, sigma = 0.05/1.2816, which is approximately 0.039 kg. Using z = 2 instead of the correct 10% tail value gives 0.025 kg, using the 5% one-tailed value z = 1.645 gives 0.030 kg, and multiplying instead of dividing gives 0.064 kg.
Derived from ZIMSEC Statistics Paper 2, November 2022, Q2
