\"- Consider a normally distributed population with a mean u = 205 and standard deviation 0 = 65. Suppose random samples of size n = 7 are selected from this population. 1. a) What is the mean of the distribution of the sample mean? b) What is the standard error of the mean? (2 decimal places) 05:- In the following questions, round the standard error and z-scores to exactly 2 (two) decimal places before determining probabilities. Report probabilities accurate to at least 4 decimal places. 2. What is the probability that a randomly selected sample mean is: a) greater than 215.3? b) less than 228.1? c) greater than 215.3 and less than 228.1? d) greater than 215.3 given less than 228.1? e) greater than 215.3 or greater than 228.1? 3. Between what values would you expect to find the middle 64% of the sample means? 3. Between what values would you expect to find the middle 64% of the sample means? Round to the nearest integer. Place the smaller value in the first box and the larger value in the second box. 4. Why are we able to use the normal distribution in the calculations above? Because the sample mean is large enough Becasuse the standard error is large enough Because the sample size is large enough Because the original population is normal