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Question $1$

Question $2$

Question $3$

Question $4$

Question $5$

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Question $7$

Question $8$

Question $9$

Question $10$

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Part $1$

The daughter of the owner of a local hamburger restaurant is preparing to open a new$$ fast$-$food restaurant called Hasty Burgers. Based on the arrival rates at her$$ father's outlets, she expects customers to arrive at the$$ drive$-$up window according to a Poison$$ distribution, with a mean of $20$ customers per hour. The service rate is$$ flexible; however, the service times are expected to follow an exponential distribution. The$$ drive$-$in window is a$$ single$-$server operation.For the service rate in part$($a$),$ what is the probability that more than four customers are in line and being$$ served?