part e only Problem 1. The Metropolis police station calls Superman an average of 3 times per hourto ask for his help. The probability that the station calls Superman in a time interval isdependent only on the length of the time interval and, furthermore, is independent of whetheror not the department called Superman on any previous time interval. Superman goes on adate with Lois Lane and picks her up from her place at 7:00pm.(a) What is the į robability that their date has been interrupted by 8:00pm?(b) If the number of times he is called is independent from one hour to the next, what isthe probability that Superman and Lois can finish their 4 hour date uninterrupted?(c) What is the probability that the date is interrupted 5 times during the first hour andLois decides to go back to the office and finish writing her article?(d) What is the probability that the date is interrupted exactly 4 times during the firsthour given that it is interrupted fewer than six times in the first hour?(e) What is the average length of time Lois waits for Superman to be called away duringthe date?

Name: part e only Problem 1. The Metropolis police station calls Superman an
Uploaded: 2024-03-20T07:06:41.000Z
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Description: part e only Problem 1. The Metropolis police station calls Superman an average of 3 times per hourto ask for his help. The probability that the station calls Superman in a time interval isdependent only on the length of the time interval and, further

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(e)
Let X be the number of calls that Superman gets from the Metropolis Police Station.
Since we are…