A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent. Let X be the number of packages that are inspected before the process is stopped.
(a) Find the mean number of packages that will be filled before the process is stopped.
(b) Find the variance of the number of packages that will be filled before the process is stopped.
(c) Assume that the process will not be stopped until four packages whose weight falls outside the specification are detected. Find the mean and variance of the number of packages that will be filled before the process is stopped.

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?