In testing lethal concentration of chemical found in polluted water, researchers have determined that certain concentration will kill 20% of the fish which are subjected to it for 24 hours. 20 fish are placed for 24 hours in the tank containing this concentration of chemical. Let X be the number of fish that are killed after 24 hours.
a. Find out the distribution of X?
b. How many fish are anticipated to be killed?
c. Find out the variance and standard deviation of X?
d. Find out the probability that exactly 6 fish will be killed?
e. Find out the probability that at most 4 fish will be killed?
f. Find out the probability that at least 2 fish will be killed?
g. Given that at most 4 fish are killed, Find out the probability that exactly 4 are killed?