5.86 The effect of sample size on the standard deviation. Assume that the standard deviation in a very large population is 100.

1. (a) Calculate the standard deviation for the sample mean for samples of size 1, 4, 25, 100, 250, 500, 1000, and 5000.

2. (b) Graph your results with the sample size on the x axis and the standard deviation on the y axis.

3. (c) Summarize the relationship between the sample size and the standard deviation that your graph shows.