An inspector selects every nth item in a production line for a detailed inspection. Suppose that the time between item arrivals is an exponential random variable with mean 1 minute, and suppose that it takes 2 minutes to inspect an item, find the smallest value of n that with a probability of 90% or more, the inspection is completed before the arrival of the next item that requires inspection. [20 points]Question 5:An inspector selects every nth item in a production line for a detailed inspection. Suppose that the time between item arrivals is an exponential random variable with mean 1 minute, and suppose that it takes 2 minutes to inspect an item, find the smallest value of n that with a probability of 90% or more, the inspection is completed before the arrival of the next ite