Question 729597
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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(6,3)*0.15^3*(1-0.15)^3}}} = {{{220*0.15^3*0.85^3}}} = 0.4560  (rounded).    <U>ANSWER</U>




(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 - (1-0.15)^6}}} = {{{1 - 0.85^6}}} = 0.6229  (rounded).    <U>ANSWER</U>
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Solved.