(Solved): Assume a Poisson random variable has a mean of 4 successes over a 112-minute period. a. Find the m ...

Assume a Poisson random variable has a mean of 4 successes over a 112-minute period. a. Find the mean of the random variable, defined by the time between successes. b. What is the rate parameter of the appropriate exponential distribution? (Round your answer to \( \mathbf{2} \) decimal places.) c. Find the probability that the time to success will be more than 58 minutes. (Do not round intermediate calculations and round final answer to 4 decimal places.)