5. Assume that the probability that a person is infected with COVID is 0.02 in your...

5. Assume that the probability that a person is infected with COVID is 0.02 in your area. If you randomly select people off the street,

(a) what is the probability that the first person to test positive is the seventh person tested?

(b) How many people would you have test before you discover your first person to test positive?

(c) If you alow plus or minus one standard deviation, what is the range you might expect the first person to test positive? (Note: For all questions, assume the test is 100 percent accurate!)

Expert Solution

    Let
   p = 0.02   probability that a person is infected with COVID

a)   Let X be the number of persons tested until the first positive (X includes the first positive)
   Then
   X ~ Geometric distribution
   To find P(X = 7)

       = 0.0177
   P(first person to test positive is the seventh person tested) =
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b)   Expected number of persons tested before discovering the first postive person
       = Expected value of the Geometric distribution

       = 50

Number of persons tested before discovering first positive =

----------------------------------------------------------------------------------------------------------------------------

c)   Variance of the geometric distribution is

       = 2450

   Standard Deviation = sqrt(2450)
       = 49.4975

   1 standard deviation plus or minus from the mean
       = 50 ± 49.4975
       = (0.5025, 99.4975)


   Range =

that is range can be 1 person or 100 persons tested for the first person to test positive

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orchestra answered 1 year ago

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