I will appreciate the assistance with the following task:
The meteorological station, which is located in the botanical garden of Sydney, registers the amount of precipitation from 1885. The average annual rainfall for the period from 1885 to 2015 inclusive is 1197.69 mm, the sample variance is 116182.2.
Considering that the annual rainfall is a random variable that does not vary in time and has a normal distribution, construct an interval that will contain the probability of 99.7% of the precipitation amount that will fall in 2016.
1.What is its upper limit? Round the answer to two characters after the decimal point.
Estimate the value of the parameter σ¯n - the standard deviation of the normal distribution, which, according to the central limit theorem, approximates the distribution of the average amount of precipitation per year from the previous problem. Round the answer to two characters after the decimal point.
Build an approximate 99.7% confidence interval for the average rainfall for the year. What is the upper limit of confidence? Round the answer to two characters after the decimal point.
According to the Central Limit Theorem, $\bar X = 1197.69$ is an observation from an approximately normal distribution. Assuming that you have independent observations over a period of $n$ years, a 95% confidence interval for the true mean annual rainfall $\mu$ would be of the style $\bar X \pm 2 S\sqrt{1/n},$ where $S$ is the sample standard deviation and $n$ is over a hundred.
A corresponding 95% prediction interval for rainfall in an additional year (not used in determining $\bar X$ or $S$) would be $\bar X \pm 2S\sqrt{1 + \frac{1}{n}}.$
I realize this is not a direct answer to your question, but it ought to be close enough to allow you to get to the relevant section in your text and make necessary adjustments for the exact question you are expected to answer.