SOLUTION: Statistics from the Port Authority of New York and New Jersey show that 70% of the vehicles using the Lincoln Tunnel that connects New York City and New Jersey use E-ZPass to pay t

Question 1202771: Statistics from the Port Authority of New York and New Jersey show that 70% of the vehicles using the Lincoln Tunnel that connects New York City and New Jersey use E-ZPass to pay the toll rather than stopping at a toll booth. Twelve cars are randomly selected.
a. How many of the 12 vehicles would you expect to use E-ZPass?
b. What is the mode of the distribution? What is the probability associated with the mode? (Hint: Mode is the value of X with the highest probability)
c. What is the probability three or more of the sampled vehicles use E-ZPass?
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Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It's a binomial with n=12 and p=0.7
the expected value is 8.4 That answers the first part.
For probability of 3 or more, do 1-prob (0,1,2)
prob of 0=0.3^12=0 essentially
prob of 1 is 12*0.7*0.3^11=0.00001
prob of 2 is 12C2*0.7^2*0.3^10=0.0002
answer is the 1-sum which is 1-0.0002=0.9998
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can check the mode 12C8*0.7^8*0.3^4=0.2311
and for 9 is 12C9*0.7^9*0.3^3=0.2397
The mode is 9.

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