A horticulturist who has just moved to Hamilton, New Zealand, and wants to measure the average spring time (note, spring is September to December in...

A horticulturist who has just moved to Hamilton, New Zealand, and wants to measure the average spring time (note, spring is September to December in the southern hemisphere) rainfall per day. After measuring rainfall for 90 days in spring, the horticulturist finds that the average rainfall per day was 3.07mm with a standard deviation of 0.93mm per day. Use this information to answer questions 4-6.

1.    Calculate the standard error of the sample mean of a sample of 90 measurements. Show your work. (5%)

2.    Create and interpret a 90% confidence interval for the mean daily rainfall. Show your work. (15%)

3.    The horticulturist decides to take more measurements in order to get a more accurate estimate. If the horticulturist wants to be able to create a 99% confidence interval for the mean daily rainfall with a margin of error equal to +/- 0.2 mm, how large should the sample be? Show your work. (15%)