Cars arrive at an inspection station according to a Poisson distribution at a rate of 10 cars per hour (λ = 10). With probability of 0.5, a car will pass inspection. a. What is the probability that at most 45 cars will arrive in the 3 hour time period? Write out the theoretical form and use R to compute a numeric value. b. Assume cars are independent of one another. What is the probability that 10 cars will arrive in a 1 hour time period AND all 10 will pass inspection. Write out the theoretical form and use R to compute a numeric value.

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