Question

One of the quirks of the ground is occasional acid fog. Only 150 grounders are immune to acid fog out of a total of 3000 grounders. For a random group of 250 grounders in an acid fog;

A. (6 points) What is the expected value and standard deviation of the number of survivors? (HINT: It might be useful to think about the Binomial distribution here.) (Your answer here)

B. (8 points) what is the approximate probability that the number of survivors is at least 20? (Your answer here)

C. (6 points) Verify the conditions needed to compute the probability in Part (B) above. (Your answer here)

Answer 1

The probability that a grounder is immune to acid fog is

A) In a random group of 250 grounders in an acid fog

The expected value of the number of survivors are = np = 250*0.05 = 12.5

the standard deviation of the number of survivors is

B)the probability that the number of the survivor is at least 20 =

c) A binomial experiment is an experiment which satisfies these four conditions:

• A fixed number of trials. Here it is 250 n= 250
• Each trial is independent of the others. Each grounder is independent of each other.
• There are only two outcomes. Either the grounder is immune to acid fog or not.
• The probability of each outcome remains constant from trial to trial.The probability that the grounder is immune to acid fog is same for each grounder i.e p =0.05