Consider a population with a mean ,1: = 165 and standard deviation 0' = 81]. Suppose random samples of size n. = 92 are selected from this population. 1. a} What is the mean of the distribution of the sample mean? l\": = b} What is the standard error of the mean? [2 decimal places} CT: = In the following questions, round the standard error and z-scores to exactly; decimal places before detem1ining probabilities. Report probabilities accurate to at least 3 decimal places. 2. What is the probability that a randomly selected sample mean is: a} greater than 156.3? \\ .r' .r' \\ b} less than 164.6? '\\ / / \\ c} greater than 156.3 and less than 164.6? \\ / .-' \\ cl] greater than 156.3 given less than 164.6? z"\\. "N .r' e} greater than 156.3 or greater than 164.6? "x X 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 rst box and the larger value in the second box. and \\ / \\ / Between 4. Why are we able to use the normal distribution in the calculations above? 0 Because the sample mean is large enough 0 Because the sample size is large enough 0 Becasuse the standard error is large enough 0 Because the original population is normal