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