1 It is required to select a random sample of 30 pupils from a school with 853 pupils. A student suggests the following method.
"Give each pupil sequentially a three-digit number from 001 to 853 . Use a calculator to generate random three-digit numbers from 0.000 to 0.999 inclusive, multiply the answer by 853 , add 1 and round off to the nearest whole number. Select the corresponding pupil, and repeat as necessary".

1. Determine which pupil would be picked for each of the following calculator outputs: $$0.103 , \quad 0.104 , \quad 0.105 , \quad 0.106 , \quad 0.107$$
2. Use your answers to part (i) to show that this method is biased, and suggest an improvement.