Consider a large population made of 1,000,000 observations (N=1,000,000). From this population, we choose 5,000 samples (with replacement). Each sample is of size 144 (n=144). Every time that a sample is selected, we compute the mean and we record it in a dataset. Ultimately, we end up with 5,000 samples. Central Limit Theorem implies that:

The standard deviation of sampling distribution of means is called: the standard error. Compute the standard error, considering the information in the above question and assuming that population standard deviation is equal to 24. (Only report the numerical value of the standard error. Round up your answer to two decimal points).

Consider the information in the last two questions. What percentage of sample means are less than 97.5, assuming that the population mean is equal to 100? (Report your answer in decimal precision (rather than percentages). Round up your answer to two decimal points).

Consider the information in the last three questions. What percentage of sample means are greater than 97.5 yet less than 100? (Report your answer in decimal precision (rather than percentages). Round up your answer to two decimal points).