I’m studying for my Statistics class and need an explanation.
1a. In a certain hospital ER the average amount of patients that enter in a 15 minute interval is 3.6. If each 15 minute interval is independent of one another, and the amount of patients that show up in one 15 minute interval does not influence or change the number of patients that show up in any other 15 minute interval. Arrivals occur smoothly throughout each 15 minute interval. Answer the following questions: (round final answers to 4 decimal places)
A. What is the probability that at most 2 patients will show up in a 15 minute interval?
B. What would be your new mean, if we were to use this information to figure out probabilities during a 5 minute interval?
C. Using the new mean in part B, what is the probability that more than 1 patient will show up in a 5 minute interval?
1b. The completion times for the government exam used for entrance into Officer Candidate School is uniformly distributed between 85 minutes and 145 minutes. (round final answers to 4 decimal places)
A. What is the probability someone finishes the exam between 95 and 120 minutes?
B. What is the probability it takes a candidate at least 110 minutes to finish the exam?
2. The average daily commuting distance for a New Yorker is 31 miles with a standard deviation of 5.8 miles. If commuting distances are normally distributed:
A. What is the probability that a person commutes at most 35 miles?
B. What is the probability that a person commute is between 25 and 38 miles?
C. What would someone have to commute to be in the top 6% of longest commutes (Where does the Top 6% start)?
MUST SHOW ALL WORK CLEARLY WITH STEPS SO I CAN LEARN IT.