That is the question I need help

Consider a normally distributed population with a mean / = 231 and standard deviation o = 86. Suppose random samples of size n = 10 are selected from this population. 1. a) What is the mean of the distribution of the sample mean? MI = b) What is the standard error of the mean? (2 decimal places) In the following questions, round the standard error and z-scores to exactly 2 decimal places before determining probabilities. Report probabilities accurate to at least 3 decimal places. 2. What is the probability that a randomly selected sample mean is: a) less than 257.7? b) greater than 252.27 c) less than 257.7 and greater than 252.2? d) less than 257.7 given greater than 252.2? e) less than 257.7 or less than 252.2? 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 original population is normal O Because the sample size is large enough O Because the sample mean is large enough O Becasuse the standard error is large enough