A manufacturing plant$$s main production line breaks down an average of $2\mathrm{.}4$ times per day. Whenever the

line goes down, it costs the company $$500$ in maintenance, repairs, and lost production. What is the

probability that the production line will break down at least $3$ times tomorrow? What is the approximate

expected value for the amount of money that production line breakdowns will cost the company each day?

The company in has disciplined a worker who was suspected of pilfering tools and supplies from the plant.

The very next day, the production line broke down $9$ times. Management has confronted the union with

accusations of sabotage on the line, but the union president says it$$s just a coincidence that the production

line happened to break down so many times the day after the worker was disciplined. Using probabilities

appropriate to your discussion, comment on how much of a coincidence this high number of breakdowns

would appear to be$.$