Question

Meteorologists have tracked the total annual rainfall in the town of Spring Valley year after year, and found that it follows a normal distribution. The average annual rainfall is 18 inches, with a standard deviation of 6 inches. In one particular year, only 9 inches of rain fell. You work for the local newspaper, and your editor has asked you to write a story about the terrible drought the town is suffering from and how dire the situation is. Write a brief paragraph that you could use to explain the statistical facts to the newspaper readers. Include a comment on whether you agree that the situation is very abnormal. Make sure you use what you are learning about the normal distribution in your newspaper article.

Answer 1

It is given that total annual rainfall in the town of Spring Valley year after year follows a normal distribution. This means that it must be following the empirical rule for normal distribution. Average annual rainfall is 18 inches, with a standard deviation of 6 inches. With normal distribution, we know that the distribution of annual rainfall must be following a bell shaped curve where 95% of the data or annual rainfall data values must be within 2 standard deviation from the average annual rainfall.

Statistical calculation for 95% data usual range, this will give us idea about the usual range for annual rainfall based on the given data values.

Lower usual limit is

Upper usual limit is

So, it is clear from the above calculation that annual rainfall between the range of 6 inches to 30 inches are usual according to normal distribution and any value outside this range,will be considered as unusual.

Therefore, the annual rainfall for the particular year with 9 inches of rainfall is not unusual and the conditions are not abnormal as we can expect this much variation in annual rainfall.