Question

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

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

(i) If a sample of 204 people is selected without replacement, what is the probability that at least 105 will be infected? Give an exact expression for your answer. Do not simplify.

(ii) Repeat Part (i) except assume that the sampling is with replacement. Do not simplify.

(iii) 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 non- overlapping groups of six]

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