Please make sure your answer is correct, Thank you!

1) Suppose you work for at a coffee shop and are studying customer purchases. Most customers purchase small inexpensive orders but a few customers purchase much larger expensive orders. You nd the average order is 9.43 dollars with a standard deviation of 7.32 dollars. (a) What is the most likely shape/ distribution for the amount of individual purchases? (1)) Assuming that on one particular day your shop had 250 purchases what is the probability that the TOTAL orders will be more than 2250 dollars? 2) Suppose that El Camino is studying the average number of hours students study for classes per week. According to research from 2010 El Camino students spent an average of 21 hours a week studying for classes. El Camino wants to study if this average has changed. To do this they take a random sample of 81 current students and nd that the average student spent 19.3 hours studying with a standard deviation of 6.4 hours. (Note: You may assume there are approximately 20,000 El Camino students). (a) Carry out a hypothesis test at a = .05 to test the claim that the average number of hours per week that El Camino students study has changed since 2010. (b) Describe what it would mean in this situation to make a Type I error (c) Describe what it would mean in this situation to make a Type II error ((1) Construct a 95% condence interval for the average number of hours studied by El Camino students per week. Make sure to interpret your interval. EXTRA CREDIT QUESTION) Look back at Question 1. What is the probability that for one week this coffee shop will have TOTAL orders more than 2250 dollar on all 7 days