In an attempt to decrease drunk driving, police set up vehicle checkpoints durin

Question

In an attempt to decrease drunk driving, police set up vehicle checkpoints during the July 4 evening. The police randomly select vehicles to be stopped for "informational" checks. On a particular roadway, assume that 20% of all drivers have a blood alcohol level above the legal limit. For a random sample of 15 vehicles, compute the following probabilities: All 15 drivers will have a blood alcohol level exceeding the legal limit. Exactly 6 of the 15 drivers will exceed the legal limit. Of the 15 drivers, 6 or more will exceed the legal limit. All 15 drivers will have a blood alcohol level within the legal limit.

Explanation / Answer

p = 0.2

n = 15

P(x) = 15Cx * 0.2x * (1 - 0.2)15-x

a) P(X = 15) = 15C15 * 0.215 * 0.80

                     = 0

b) P(X = 6) = 15C6 * 0.26 * 0.89

                   = 0.043

c) P(X > 6) = 1 - P(X < 6)

                  = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

                  = 1 - [15C0 * 0.20 * 0.815 + 15C1 * 0.21 * 0.814 + 15C2 * 0.22 * 0.813 + 15C3 * 0.23 * 0.812 + 15C4 * 0.24 * 0.811 + 15C5 * 0.25 * 0.810 ]

                  = 1 - 0.9389

                  = 0.0611

d) P(X = 0) = 15C0 * 0.20 * 0.815

                  = 0.0352

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