1 40pts A national standardized test is such that 20 of all

1 .(40pts) A national standardized test is such that 20% of all test takers receive a score below passing. I select 5 participants at random and administer the test. Let Y = the number of students that fail the test in my sample. Answer the following: a) Argue this constitutes a binomial experiment by discussing how the requirements are fulfilled. b) Identify n, p, (1-p) c) Determine the following probability: P(exactly I fails), Determine the Expected number of failures.

Solution

(A) It is a binomial experiment because all requirement are met.

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(B) n=5 and p=0.2 and q=1-p=1-0.2=0.8

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(C) P(X=x)=5Cx*(0.2^x)*(0.8^(5-x)) for x=0,1,2,..,5

So the probability is

P(X=1) =5C1*(0.2^1)*(0.8^(5-1)) =0.4096

expected = n*p= 5*0.2 =1