Consider a population with a mean ,u, : 205 and standard deviation or = 66- Suppose random samples of size n = 9? are selected from this population. 1. a] What is the mean of the distribution of the sample mean? is = l i b] What is the standard error of the mean? {2 decimal places] Ja=l l 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) less than 205.3? b) greater than 197.7? c) less than 205.3 and greater than 197.7? d) less than 205.3 given greater than 197.7? e) less than 205.3 or less than 197.7? 3. Between what values would you expect to find the middle 62% 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. Between and 4. Why are we able to use the normal distribution in the calculations above? O Because the sample size is large enough O Because the sample mean is large enough O Becasuse the standard error is large enough O Because the original population is normal