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# A horticulturist has just moved to Hamilton, New Zealand, and wants to measure the average springtime rainfall per day (Note: Spring is from...

A horticulturist has just moved to Hamilton, New Zealand, and wants to measure the average springtime rainfall per day (Note: Spring is from September to December in the Southern Hemisphere). 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 solve the following and **show all work**.

a. Calculate the standard error of the sample mean of a sample of 90 measurements.

b. Show and interpret a 90% confidence interval for the mean daily rainfall.

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