Question

Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water

Answer 1

Answer:

$Var = 1.9$

Step-by-step explanation:

Given

$p = \frac{1}{20}$  i.e. 1 per 20cc of water

$n = 40$ -- sample size

Required

The variance

This is calculated using:

$Var = np(1 - p)$

So, we have:

$Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})$

$Var = 40 * \frac{1}{20} * \frac{19}{20}$

$Var = 2 * \frac{19}{20}$

$Var = \frac{38}{20}$

$Var = 1.9$