SOLUTION: It has been reported that 15% of all cars on the highway are traveling at speeds in excess of 65 mph. If the speeds of six random automobiles are measured via radar: a. What is t

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Question 729597: It has been reported that 15% of all cars on the highway are traveling at speeds in excess of 65 mph. If the speeds of six random automobiles are measured via radar:
a. What is the probability that exactly 3 cars are speeding?
b. what is the probability that at least one car is going over 65 mph
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53339) About Me  (Show Source):
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It has been reported that 15% of all cars on the highway are traveling at speeds in excess of 65 mph.
If the speeds of six random automobiles are measured via radar:
a. What is the probability that exactly 3 cars are speeding?
b. what is the probability that at least one car is going over 65 mph
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(a)  This problem is on binomial distribution.

     Use the formula for n=6 trials, k=3 success and the probability of the individual success

     p = 0.15 in each individual trial


         P = C%286%2C3%29%2A0.15%5E3%2A%281-0.15%29%5E3 = 220%2A0.15%5E3%2A0.85%5E3 = 0.4560  (rounded).    ANSWER




(b)  The probability in case (b) is the complement to the probability that all 6 cars are going slower than 65 mph


         P(at least one r...)  = 1+-+%281-0.15%29%5E6 = 1+-+0.85%5E6 = 0.6229  (rounded).    ANSWER

Solved.