1. As a healthcare analyst for a large regional hospital in Mendocino County, you have been tasked with researching how to best allocate limited space in the operating room recovery wing. In patients who undergo laparoscopic surgery, the incidence of post-operative infection is 7%. The length of hospital stay for patients who develop an infection following laparoscopic surgery can be modeled by a normal distribution with a mean of 5 days and a standard deviation of 1.5 days. Present your answers rounded to two decimal places and present answers as proportions, e.g. (.40) rather than percents (40.00 %)

1.1) What is the probability that an infected patient's length of stay will be greater than 8 days?

1.2) What is the 80th percentile in stay length for a patient given that they have a post-operative infection?

1.3) What is the probability that the average stay length of the next 3 infected patients is less than than 6.5 days?

1.4) What is the probability that a patient is infected and then stays for 4 to 5 days?