Suppose that only 35% of all drivers come to a complete stop at an intersection

Question

Suppose that only 35% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. Suppose 12 drivers coming to such an intersection under these conditions are randomly selected.

a What is the probability that exactly 7 drivers in the sample will come to a complete stop?

b What is the probability that fewer than 5 drivers in the sample will come to a complete stop?

c What is the probability that between 4 and 7 (inclusive) drivers in the sample will come to a complete stop?

Explanation / Answer

n = 12

p = 0.35

It is a binomial distribution.

P(X = x) = nCx * px * (1 - p)n - x

a) P(X = 7) = 12C7 * (0.35)^7 * (0.65)^5 = 0.0591

b) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(x = 3) + P(x = 4)

                  = 12C0 * (0.35)^0 * (0.65)^12 + 12C1 * (0.35)^1 * (0.65)^11 + 12C2 * (0.35)^2 * (0.65)^10 + 12C3 * (0.35)^3 * (0.65)^9 + 12C4 * (0.35)^4 * (0.65)^8

= 0.5833

c) P(4 < X < 7) = P(X = 4) + P(X = 5) + P(x = 6) + P(x = 7)

                        = 12C4 * (0.35)^4 * (0.65)^8 + 12C5 * (0.35)^5 * (0.65)^7 + 12C6 * (0.35)^6 * (0.65)^6 + 12C7 * (0.35)^7 * (0.65)^5 = 0.6278

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