Question

The amount of water a construction worker consumes in a day is normally distributed with a mean of 2.7 litres, and a standard deviation of 0.4 litres.
Construction workers carry water bottles containing 3 litres.
(a) What is 20th percentile of this distribution (i.e. 80% of workers will consume more than this volume)?
(b) What is the probability of a randomly selected construction worker consuming his/her bottle of water in a day?

(c) Management is considering letting teams of two construction workers share their two bottles of water. If this is done, what proportion of teams (of two) will consume all of their water in a day?

(d) What is the most important assumption you have made in answering part (c)? Comment briefly on whether you think this is a reasonable assumption or not.

Answer 1