A camp director is interested in the mean number of letters each child sends during his or her camp session. The population standard deviation is known to be 2.5. A survey of 20 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8.

a. i. x - =________ ii. σ =________ iii. n =________

b. Define the random variables X and X - in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 90% confidence interval for the population mean number of letters campers send home.

i. State the confidence interval.

ii. Sketch the graph.

e. What will happen to the error bound and confidence interval if 500 campers are surveyed? Why?