Question

A particular concentration of a chemical found in polluted water has been found to be lethal to 10% of the fish that are exposed to the concentration for 24 hours. 300 fish are placed in a tank containing this concentration of chemical in water.

a. Find the mean and variance of the number that survive.

b. Find the mean and variance of the number that do not survive

Answer 1

Solution :

Given that,

a) p = 0.10

q = 1 - p = 1 - 0.10 = 0.90

n = 300

Using binomial distribution,

Mean = = n * p = 300 * 0.10 = 30

Variance = ² = n * p * q = 300 * 0.10 * 0.90 = 27

b) p = 1 - 0.10 = 0.90

q = 1 - p = 1 - 0.90 = 0.10

n = 300

Using binomial distribution,

Mean = = n * p = 300 * 0.90 = 270

Variance = ² = n * p * q = 300 * 0.90 * 0.10 = 27