Consider a population with a mean =166 and standard deviation=60. Suppose random samples of sizen=53 are selected from this population.

1. a) What is the mean of the distribution of the sample mean?

x=.......................

b) What is the standard error of the mean? (2 decimal places)

1. x=.................

In the following questions, round the standard error andz-scoresto exactly2 decimal placesbefore determining probabilities. Report probabilities accurate to at least 3 decimal places.

2 What is the probability that a randomly selected sample mean is:

1. a) greater than 158.7?
2. b) less than 171.4?
3. c) greater than 158.7 and less than 171.4?
4. d) greater than 158.7 given less than 171.4?
5. e) greater than 158.7 or greater than 171.4?

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...................and.................

4 Why are we able to use the normal distribution in the calculations above?

• Because the standard error is large enough
• Because the original population is normal
• Because the sample size is large enough
• Because the sample mean is large enough