Meteorologists have tracked the total annual rainfall in the town of Spring Vall

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. 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.

Explanation / Answer

Mean= 18.00
sd= 6.00

P(X<9)

I know that, z = (X-mean)/(sd)
z1 = (9-18)/6)
z1=-1.5000

The Z score tells the number of standard deviations away from the mean. this year the rainfall is 1.5 units less than the mean rainfall.

hence,
P(X<9)
=P(Z<-1.5)
NORMSDIST(-1.5)
0.0668

there 6.68% chances that rainfall will be less than 9 inches.

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