Question

In testing the lethal concentration of a chemical found in polluted water. it is found that a certain concentration will kill 20% of the fish that are subjected to it for 24 hours. if 20 fish are placed in a tank containing this concentration of chemical. find the probability that after 24 hours :______a) Exactly 14 fish survive ? b) at least 10 survive ? c) at most 16 fish will die ?

Answer 1

a) 0.1091

b) 0.9994

c) 0.5886

Explanation:

X = the number of fish out of 20 that die after 24 hours

x = 0, 1, 2, . . . , 20

X~ Binomial (n= 20, p =0.20)

P(14 survive) = P(X = 6)

=
`nC_r p^r q^(n-r)= 20C_6 0.2^6*0.8^(14)`=0.1091

Similarly we can find out

P(at least 10 survive) = P( X <= 10 ) = (Using technology) = 0.9994

P(at most 16 will survive) = P(X <= 16) = (Using technology) = 0.5886