Question

A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty randomly selected fish are placed in a tank containing this concentration of chemical in water. a. Demonstrate that X is a binomial random variable where X is the number of fish that survive. _____________________________________________ _____________________________________________ ___________________________________________(3) Find the following probabilities: b. More than 10 but at most 15 will survive. ______________________________(2) c. Exactly 10 will survive. ______________________________(2) d. At least 8 but less than 12 will not survive. ______________________________(2) e. More than 9 but less than 16 will not survive. _____________________________(2) f. What is the mean number of fish that will survive? Use the correct notation. _____________________________(3) g. What is the standard deviation for this probability distribution? Use the correct notation. _____________________________(3) h. Find ?(µ +  > X) for X = the number of fish that survive. ________________

Answer 1

a)

Let X is a number fishes survive

probability of fish die q = 0.2

therefore probability of fish survive is p = 0.8

p.m.f of X is

3)b) more than 10 but at most 15

P(10<X 15) = P(11 X 15) =

2c)

(2) d. At least 8 but less than 12 will not survive

P( 8 X<12) = P(8X11) =

_(2) e. More than 9 but less than 16 will not survive

P(9<X<16) = P(10X15) =

(2) f. What is the mean number of fish that will survive?

g. What is the standard deviation for this probability distribution?