CFA Practice Question

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CFA Practice Question

It is estimated that 70% of motorists on a certain stretch of highway exceed the speed limit. A highway patrolman with a radar device randomly selects 15 motorists on this part of the highway and checks their speed. What is the probability that at least 13 are caught speeding?
A. 0.092
B. 0.128
C. 0.908
Explanation: We use the binomial distribution with n = 15 and pai = 0.7 to get P(X>= 13) = p(13) + p(14) + p(15) = 0.092 + 0.031 + 0.005 = 0.128.

User Contributed Comments 9

User Comment
haarlemmer My caculation shows that the answer is 0.1268, hehe. Afterall, it is the nearest.
dimos The key is "at least"
chamad how to get p(13)=0.092?...thanks
Yurik74 Chamad: [15!/(13!*2!)]*(.7^13)*(.3^2)
Sebgati or 15C13 * 0.7^13 * 0.3^2
boddunah messed it up on calculation part. dang it
enetis on the exam these calcs would take at 3-4 valuable minutes.... tough call.
birdperson enetis: it shouldnt take that long...

15C13 * (.7)^13 * (.3)^2 +
15C14 * (.7)^14 * (.3)^1 +
15C15 * (.7)^15 * (.3)^0

there are even some ways to take shortcuts in there... good luck
dbalakos Do not do all the calculations. Find that P(13) = 0.092, so you already know that answer A is not correct. Multiply 0.092 with 3 and you will find something larger than 0.128 and smaller than 0.908. So, you have found the right answer the smaller one, B.
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