Ms. H. R. Cutt runs a one-person hair salon. She does not make appointments, but runs the salon on a first-come, first-served basis. She finds that she is extremely busy on Saturday mornings, so she is considering hiring a part-time assistant and even possibly moving to a larger building. Having obtained a master's degree in operations management (OM) prior to embarking upon her career, she elects to analyze the situation carefully before making a decision. She thus keeps careful records for a succession of Saturday mornings and finds that customers seem to arrive according to a Poisson process with a mean arrival rate of 5 per hour Because of her excellent reputation (what else would you expect from someone with an M.S. in OM?), customers were always willing to wait. The data further showed that customer processing time (aggregated female and male) was exponentially distributed with an average of 10 min.
a) Cutt first decided to calculate the average number of customers in the shop and the average number of customers waiting for a haircut.
b) Cutt is also interested in the percentage of time an arrival can be served right away without having to wait at all.
c) Cutt is interested in the probability that there are at least 4 customers in her hair salon.