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Police records in the town of Saratoga show that 13 percent of the drivers stopp

ID: 3303921 • Letter: P

Question

Police records in the town of Saratoga show that 13 percent of the drivers stopped for speeding have invalid licenses. If 11 drivers are stopped for speeding, find the probabilities that

  

None will have an invalid license. (Round your answer to 4 decimal places.)

Exactly three will have an invalid license. (Round your answer to 4 decimal places.)

At least 4 will have invalid licenses. (Round your answer to 4 decimal places.)

  

Police records in the town of Saratoga show that 13 percent of the drivers stopped for speeding have invalid licenses. If 11 drivers are stopped for speeding, find the probabilities that

Explanation / Answer

This is Bin(n,p) distribution where n = 11 , p = 0.13

That is x ~ Bin(11, 0.13)

Binomial probability distribution is

p(x) = nCx px (1-p)n-x

a)

p(x = 0) = 11C0 0.130 (0.87)11-0

= 0.2161

b)

p(x = 3) = 11C3 * 0.133 (0.87)11-3

= 0.1190

c)

p(x>=4) = 1 - p(x<=3)

= 1 - [ p(x=0) + p(x=1) + p(x=2) + p(x=3)]

= 1 - [ 11C0 * 0.130 (0.87)11-0 + 11C1 * 0.131 (0.87)11-1 + 11C2 * 0.132 (0.87)11-2 +11C3 * 0.133 (0.87)11-3 ]

= 1 - 0.95577

= 0.0442