Consider a population with a mean =212=212 and standard deviation =78=78. Suppose random samples of size n=78n=78 are selected from this population.

1. a) What is the mean of the distribution of the sample mean? x=x= b) What is the standard error of the mean? (2 decimal places) x=x=
2. What is the probability that a randomly selected sample mean is: a) less than 206.1? b) greater than 202.8? c) less than 206.1 and greater than 202.8? d) less than 206.1 given greater than 202.8? e) less than 206.1 or less than 202.8?
3. Between what values would you expect to find the middle 76% 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 and .
2. Why are we able to use the normal distribution in the calculations above?