Q1) In testing lethal concentration of chemical found in polluted water, researchers have found out that certain concentration will kill 20% of fish which are subjected to it for 24 hours. 20 fish are placed for 24 hours in tank containing this concentration of chemical. Let X be number of fish that are killed after 24 hours.

a) Determine the distribution of X ?

b) Find the number of fish which are expected to be killed?

c) Determine the variance and standard deviation of X ?

d) Find out the probability that exactly 6 fish will be killed?

e) Determine the probability that at most 4 fish will be killed?

f) Compute the probability that at least 2 fish will be killed?

g) Given that at most 4 fish are killed, determine the probability that exactly 4 are killed?