Question

3. Among the people who take a Covid-19 test in Arizona, 21% test positive for the disease. If one is in Arizona standing in a line to receive a Covid-19 test with a total of 40 people in the line, what's the probability that a. exactly 8 people in the line will test positive? Round answer to 3 significant digits. b. at least 8 people in the line will test positive? Round answer to 3 significant digits.

Answer 1

Let X denote the number of people who tests positive for the disease

n = 40, p = 0.21

np = 40*0.21 = 8.4

np(1 - p) = 6.636

Since np(1 - p) > 5, X can be approximated to Normal distribution with Mean = 8.4 and Standard deviation = √6.636 = 2.576

(a) The required probability = P(X = 8)

= $\binom{40}{8}*0.21^{8}*0.79^{32}$

= 0.154

(b) The required probability = P(X ≥ 8)

Using correction of continuity, P(X ≥ 8) = P(X > 7.5)

= P{Z > (7.5 - 8.4)/2.576}

= P(Z > -0.35) = 0.637