a) A lake contains a population of trout with a mean weight of 800 g and a standard deviation of 100 g. A fisherman catches the maximum allowed number of fish every day. On any given day there is a 68.3% chance that the mean weight of fish he catches will be between 750g and 850g. What is the maximum allowed number of fish?

b) An R data frame called "NPKgrowth" contains two columns with 150 rows. The first column named "fertilizer", contains fertilizer types: 50 rows of each of "N", "P" and "K" respectively. The second column, named "growth", contains dry weights (g) of plants grown with each fertilizer type in an experiment. Write the R code that will enable you to

• carry out an analysis of variance on the effect of fertilizer type on plant growth
• conduct a Tukey post-hoc test on the same data
• construct a box plot showing the data, with the X and Y axes labeled "Fertilizer Type" and "Plant Dry Weight (g)", respectively.

c) A seed company sells packages of cilantro seeds with an average of 550 seeds per package. You wish to know the probability that a package will contain at least 530 seeds, but you don't know the standard deviation of the number of seeds per package. Your colleague has calculated a standard deviation for a sample of 10 seed packages. He suggests you use that standard deviation to calculate a Z score, and then refer to the standard normal distribution to find out what you want to know. Explain the problem with his suggestion and how you might use the data he has provided more effectively.