1. The local government is considering applying cost cutting measures to the number of hours its 811 line is open daily. Currently it is available 24 hours a day, 7 days a week. To help with the decision making process, the government is interested in examining the average number of calls received between 11:30pm on Saturday night and 5:00am Sunday morning. A study of 10 random such time periods from 2021 revealed that the average number of calls was 4.3 with a known population standard deviation of 11.456 calls.

(a) Predict with 95% confidence the true (population) average number of calls expected to be received during this studied time period.

(b) Without performing a hypothesis test: The government is going to reduce hours if they find that the average number of calls was under 10 calls per night. How does your interval support or fail to support their decision to reduce hours?

(c) If the government wanted a maximum margin of error of 4 calls, how many sample days would they need to have? (e) Were any assumptions needed to answer the above questions. Why or why not?