According to a survey conducted at the local DMV, 50% of drivers who drive to wo

Question

According to a survey conducted at the local DMV, 50% of drivers who drive to work stated that they regularly exceed the posted speed limit on their way to work. Suppose that this result is true for the population of drivers who drive to work. A random sample of 12 drivers who drive to work is selected. Use the binomial probabilities table (Table I of Appendix B) or technology to find to 3 decimal places the probability that the number of drivers in this sample of 12 who regularly exceed the posted speed limit on their way to work is a. at most 6 Probability = b. 7 to 9 Probability = c. at least 6 Probability =

Explanation / Answer

p = 0.5

n = 12

P(X = x) = 12Cx * 0.5x * (1 - 0.5)12-x

a) P(X < 6) = 0.6128

b) P(7 < X < 9) = P(X < 9) - P(X < 6)

                         = 0.9807 - 0.6128

                         = 0.3679

c) P(X > 6) = 1 - P(X < 5)

                  = 1 - 0.3872

                  = 0.6128

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