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Answer: A Binomial distribution apply when we have n identical and independent events with two possible results, success or fail, and a probability p of success and 1-p of fail. Then, the probability that from the n events, x are success is:
Then, the number of motorist driving more than 5 miles per hour over the speed limit follow a Binomial Distributions, because we have 4 randomly selected motorists with two possible options: they are driving more than 5 miles per hour over the speed limit or they aren't, and the probability that they are driving more that 5 miles per hour over the speed is 0.4.
Finally, the probability P that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit is:
P = P(1) + P(2) + P(3) + P(4)
Where n is equal to 4 and p is equal to 0.4. Replacing the values for every x, we get:
Finally, P is equal to:
P = 0.3456 + 0.3456 + 0.1536 + 0.0256
P = 0.8704
Explanation: