Consider a normally distributed population with a mean =214=214 and standard deviation =87=87. Suppose random samples of size n=7=7 are selected from this population.

1. a) What is the mean of the distribution of the sample mean? x== Correct b) What is the standard error of the mean? (2 decimal places) x==Correct
2. What is the probability that a randomly selected sample mean is: a) greater than 219.6? Incorrect b) less than 273.2? Correct c) greater than 219.6 and less than 273.2? Correct d) greater than 219.6 given less than 273.2? Correct e) greater than 219.6 or greater than 273.2? Correct
3. Between what values would you expect to find the middle 54% 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.

1. Between Correct and Correct.
2. Why are we able to use the normal distribution in the calculations above?