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Suppose in a city of 10 million people, fifty percent have been infected with the new...

Suppose in a city of 10 million people, fifty percent have been infected with the new corona virus.Suppose that you test the 204 people one-by-one with replacement. Consider the event E that you will observe at least 6 people in a row who test positive or at least 6 people in a row who test negative. Prove that P(E) > 0.60. [Hint: Consider adjacent nonoverlapping groups of six]

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Answer #1

This is a binomial distribution question with
n = 204
p = 0.5
q = 1 - p = 0.5
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that



The z-score at x = 5.5 is,

z = -13.5128
This implies that

P(E) is very close to 1 and definitely greater than 0.6
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