1) An analyst is conducting a hypothesis test to determine if the mean time spent on investment research by portfolio managers is different from 3 hours per day. The test uses a random sample of 64 portfolio managers, where the sample mean time spent on research is found to be 2.5 hours. The population standard deviation is 1.5 hours. What is the 99% confidence interval for the population mean time spent on investment research by portfolio managers?

2) Service time at Mc Donald restaurant follows a normal distribution, with a mean of 5 minutes and standard deviation of 1 minute. The restaurant's policy is that if a customer is not served within a maximum time period, they would not be charged for the food ordered. The management wishes to provide this incentive program to at most 10% of the customers. What is the maximum guaranteed waiting time should be set at?

3) Sand is packed into bags which are then weighed on scales. It is known that if full bags of sand are intended to weigh kg, then the weight recorded by the scales will be normally distributed with a mean kg and a standard deviation of 0.36kg. A particular bag of sand was weighed four times and the weight recorded each time was different. The sample mean weight was recorded as 34.7kg. What is a 95% confidence interval for the true weight of the full bag of sand?

4) The admissions office at a college reported that this year's freshman class had an average SAT score of 1103 with standard deviation of 95. What is the probability that a sample of 40 students from this year's freshman class had average score greater than 1100?